Not a real answer, just a personal comment.
I agree with the accepted answer, however I would like to point out that this is very informal. Ending an email with only the word "désolé" is very abrupt.
It's exactly the same as using only the word "sorry" in english .
In a professionnal context, I would write why I am sorry. For example:
Désolé de ne pas pouvoir être là.
Désolé du dérangement.
Furthermore, adding a
Before the signature cannot be bad.
According to the kind of relation you have with the other person, it might sound a little bit inappropriate. If you answer one of my request so laconically, I am not sure I would recontact you again. But actually I think it is the same in english.
I would consider an email saying
I will not be available the weekend of July 20.