I'm so sorry, but I'm going to have to miss your party on (date). I know I told you I would make it, but I'm being asked to go out of town for work. There's not much I can do about this. I promise to make it to your next party.
Sincerely,
(your name)
Dear (recipient's name),
I'm so sorry, but I'm going to have to miss your party on (date). I know I told you I would make it, but I'm being asked to go out of town for work. There's not much I can do about this. I promise to make it to your next party.
Sincerely,
(your name)