I hope this letter finds you well.
apologise for missing the birthday celebration
I am truly sorry for missing your birthday celebration. It was never my intention to let you down, and I feel terrible about not being there to celebrate with you. I understand how important it is to have friends by your side on special occasions, and I regret not being able to be there for you.
explain why you missed it and why you didn't tell your friend
Unfortunately, I had a family emergency that required my immediate attention on the day of your celebration. I was caught up in dealing with the situation and completely lost track of time. By the time things settled down, it was too late to reach out to you, and for that, I apologize. I should have informed you beforehand, and I am truly sorry for not doing so.
and say what you would like to do to show that you are sorry
To make it up to you, I would like to take you out for a belated birthday dinner. I want to spend some quality time with you to show how much our friendship means to me. Please let me know a date that works for you, and I will make the necessary arrangements. I value our friendship, and I want to make sure you know how sorry I am for missing your celebration.
I look forward to seeing you soon and making it up to you. Take care.
