Gordon's first-person letter was posted on a website called Medium.
He directs it to his critics, especially Charles Barkley, and ESPN analysts Stephen A. Smith and Cris Carter, all of whom have expressed serious concern for Gordon's future and well-being, with Barkley saying Gordon's actions could lead to a premature death.
Gordon continued on the offensive at the end of his letter with a message for his critics who said his life would end badly if he maintained a reckless lifestyle.
"If you see me someday, Chuck, Stephen A., Cris, or any other well-intentioned person to whom this letter is directed, please come on over, shake my hand, and say hello," he wrote. "I won't be holding a grudge, but I will expect you to admit you were wrong about me."
Gordon explained his conditions for alcohol testing and his failed test in the letter, saying it came on a flight he took with teammates and former receivers coach Mike McDaniel on Jan. 2.
Gordon wrote: "On Jan. 2 of this year, just days after our season ended earlier than we all had hoped -- and yes, my actions during the prior offseason definitely contributed to our failure to make the playoffs; it killed me seeing our guys fight so hard when I wasn't out there with them -- I boarded a private flight to Las Vegas with several teammates. During the flight, I had two beers and two drinks. It was the first time I had consumed so much as a drop of alcohol since July 4, 2014, the day of (his DWI arrest in North Carolina)."
Gordon explained his 10-game suspension by saying eight games was for a failed marijuana test caused by "inadvertently inhaling second-hand marijuana smoke" last offseason.
He said the league agreed to reduce a four-game suspension for DWI to two because his blood-alcohol level was .01 over the legal limit.
But as a condition of being reinstated in Week 12, Gordon agreed to abstain from drinking the rest of the season and to submit to ongoing alcohol tests.
"Did I think that was excessive given I had never had any issue whatsoever with alcohol?" Gordon wrote. "Yes. Did I think it was hypocritical that a professional league making hundreds of millions of dollars off beer sponsorships was telling me not to drink? Yes. Did I so much as blink at the condition? No."
He said he was given notice he had to take a drug test as soon as he landed in Las Vegas.
"I failed the test, obviously, and the rest is history ... colored by media speculation and faux outrage," Gordon wrote. "In the end, of course, I failed myself. It doesn't matter if I thought that the league-imposed restriction on drinking had expired at the end of the regular season; what matters is that I didn't confirm whether or not that was the case. Now, that oversight has further jeopardized my relationship with my team and our fans, my reputation, and maybe even my career."
A spokesman for the Browns said the team had no comment on the letter.
Teammate Phil Taylor posted several tweets in defense of Gordon, along them saying: "Don't judge someone if you do not know them! I believe in my teammate as former Baylor Bears and now Cleveland Browns."
Gordon said that people who know him know he is "not much of a drinker."
"Even calling me a social drinker would be an exaggeration, but at that moment, on that flight, I made a choice," he wrote. "The wrong choice, as it turned out."
Gordon did not hide from responsibility for any of his failed tests.
"Words cannot express the remorse and regret I feel over this latest incident," he wrote. "I acknowledge that the repeated transgressions that have led up to this point have damaged my credibility, and for that, the only person to blame is me.
"I have let down many in Cleveland -- my Browns teammates, our hard-working coaching staff, the team's ownership, and the loyal fan base that wants nothing more than to win. Playing there is different than in many other cities. We feel the fans' pain. We know how important this is to them.
"Also, I have disappointed the family and close friends who have always stood by me -- no matter how tough things have been at certain points in my life. Believe me, there have been more dark days than I care to remember.
"Most importantly, I have failed myself. Again."
Gordon said he started using marijuana while growing up in the tough environs of Fondren in Houston, an area he described as one filled with "poverty, gang violence and very little in the way of guidance or support."
His father was not present, and his mother raised him and his two brothers. He wrote there were times he was left without guidance and supervision. Marijuana was part of the lifestyle in Fondren, he wrote.
"Again," he added, "I make no excuses for my past. That culture didn't make me do anything I didn't want to do, but when you judge me without actually knowing me, you deny the existence of the world I come from."
He wrote he wasn't ready for college, and that his problem is he is 23 with "a lot left to learn."
"I've come a long way from those mean Fondren streets, but it's clear that I can be a better me -- one who kids coming up to me for selfies and autographs can be proud of," Gordon wrote. "I want that future for myself. And I truly believe that what I am going through right now will only make me stronger. I believe that my future is bright."
He wrote he had not drank since his DWI, and had not smoked marijuana since before he was a second-round pick in the supplemental draft by Cleveland in 2012. Gordon emphasized that though he had failed, he had also succeed by rising above the circumstances of his youth.
How did he get to the point where he may face a one-year ban?
"That's easy," he wrote. "I messed up."