Just to reiterate what lvoss said, if you want suggestions on how to keep him in your family, we can help you with that. Lots of dogs stay in their crates while their owners work, and then enjoy a busy life with them when they are home.
If you have decided that you just think he would truly be better off somewhere else, then BRAT can help you with that.
In my opinion, you don't need to give up your dog because you both work full time…but if either one of you doesn't want to cope with having a dog, then rehoming is the best option.