Honestly, there is nothing you can do other than tell him that you are sorry and it was a stupid mistake.
My wife, fiance at the time of this event, did the exact same to me when i was deployed and I did not find out until a couple months ago. Me being deployed and her not cheating on me was the base of our marriage. You are right on the fact that the trust is gone. It is up to him now if he wants to try to trust you again.

Best of luck