Think of the relationship between the letter and the envelope.
1. Which by itself means absolutely nothing inside a bracket in this sentence.
2. You put the application *in* the envelope. You can't use of or on. You don't put the application on the envelope, you don't put it of the envelope. With which could be used, but without using brackets.
Enclosed with this letter is a pre-addressed, stamped envelope with which to mail your application for membership to our club.