Dear Mrs. Trechane.
After reflecting on my actions and the results they caused you, I humbly decided to write this letter where I acknowledge my mistake, I apologize to you and say that I am determined to accept the consequences of my actions.
I don't want to justify my actions, or try to take my guilt away, but I want to be as direct as possible when I say that I want to reach your forgiveness and not repeat my wrong acts. I will look for you, to give you my excuses personally and hope that in the future, we will be able to work together again, where I promise that I will be a better person.
Graciously,
Jake.