It sounds as if you may be confusing some terms. We're assuming that the letter said transvestite and not transsexual. You may want to check, since the terms mean very different things. Most transvestites are married, heterosexual, and behave and look like men in every other area of their lives. You may not have thought about your brother being gay because he probably is not.
Transvestites become excited by wearing articles of clothing usually worn by the opposite sex.
Sometimes they wear only one feminine article of clothing, but some may wear wigs, makeup and clothing. They usually dress up in private and often take great care not to be discovered by people they know. There is no surgery involved in this, and transvestites say they do not want to be a woman, they just want to wear women's clothing every now and then. It is not known why some people engage in these behaviors. Studies have shown that transvestites tend to be the oldest or the only child.