There are several ways:
1- search this forum (or pretty much any BMW forum for this subject)- not to be a jerk, but it's covered on a regular basis. Basically- jack up the rear of the car, take the parking brake off and make sure the tranny is in neutral. Rotate one of the rear wheels, if the other rear wheel rotates in the same direction, you probably have LSD, if it rotates in the opposite direction, you probably have an open diff. If you have any doubt, you'll have to take the rear cover off and have a look to see if you have the LSD clutch pack or just the regular spider gears (open diff).
2- if the metal tab is still intact, try scraping it with a knife or other sharp object to get some of the crust off it, the numbers are stamped in the steel tag, so they should show up with some scraping. Get a flashlight in there too, they are hard to read.
I would vote for #2 as the easiest.
Bret