I have found out that someone is searching for me online.  I have their IP address.  Is there a way to find out their email address from this?

Nope. They could be using a webmail email address or they can choose any prefix to their ISP domain (since the closest you'll get is their ISP's name and location).

They can also be hiding behind a cloaking service so the IP address you see is not really their IP address.