Edwin was an unhappy and abusive alcoholic who was married to Marianne Booth. They had two sons, Seeley and Jared. Seeley mentioned that Edwin was a member of the U.S. Military who flew fighter planes during the Vietnam War. Booth mentioned that the fighter jets Edwin drove were Thuds and Phantoms in The Woman in Limbo. It is possible that, like Seeley Booth's gambling addiction, Edwin drank to deal with the trauma he suffered in Vietnam. His excessive drinking eventually led him to abuse his family.
He was abusive to his wife and his sons. He once threw her down a flight of stairs. When Edwin's father, Hank, found out that was happening he prevented Edwin from seeing either son ever again, and raised the children as his own.
In The Male in the Mail, Hank revealed that Edwin passed away from liver failure because of his addiction to alcoholic beverages. Before he died, he left a letter to Hank and a box filled with his good memories with Seeley to Seeley. He seems to have left nothing for Jared or Marianne Booth.
From Edwin's Letter to Hank Edit
".... I didn't write a letter to Seeley because I knew he'd rip up anything I'd send him. And he should. If you can find a way, let him know I loved him. He and Jared deserved a better father than me. A father as good as I had. Thank you for raising him to be the man I could never be...."