Wow, what a bombshell!
I would do a google search and try to track him and the mother down. I wouldn't initiate contact until you have some idea of what their family life is like and what their life circumstances are. There could be great resentment on both of their parts for your father not supporting them.
Or, the mom may have remarried/hooked up with someone else and said that the son was that guys child. This would rock their world to find out that you and your family are the half-siblings. You need to really think this through.
Do you know the Mom's full name? Perhaps look for death notices to start. Work backward. Ask your brother as much info as you can to try to determine what he really knows. And your Mother. What did/does she know? Why now after all these years is this being brought up? Did someone contact her?
Try not to make an emotional decision or go to quickly. I can only imagine the emotions you are experiencing.