What could it be when a check engine light comes on on a BMW 528I 1998?

The "Check Engine" light on a '98 528i can come on for a whole bunch of reasons. And it takes a diagnostic computer to "look" at the onboard diagnostics and "read" the computer's report of the problem. (It presents as a "code" which requires interpretation.) Most garages, both dealers and Indy repair shops, have these computers. (Modest ones cost less than a hundred bucks.) There are even some places that will do a free "reading" for you (in the hopes of obtaining your business). Make some calls. Oh, and good luck.