Dear {Recipient}
Please accept this letter as my formal apology for what happened on {location, event, issue, etc…} on{MM/DD/YYYY}.
It was not my intention to cause any damage or inconvenience. In retrospect, I believe the situation resulted from{cause}. While this is by no means an excuse for {my behavior, what happened, etc…}, knowing the cause will help me guard against future mistakes.
Again, I am sorry for what happened. If you would like to continue this conversation, please feel free to call me at{phone}. I look forward to hearing from you and putting this matter behind us.
Sincerely,
{Sender}
{Sender}