If they are loose it usually shows up as a very distinct clunk under initial acceleration or deceleration. Mine were very annoying because my 300E is a manual transmission car, but I expect it would be noticable with an automatic.
To change them you absolutely must have a puller. You can't drive them out with a hammer because you will destroy the sheet metal carrier. My brother in law is my tech at the dealer and loaned me a puller that he made. It worked great.
You can buy a good puller from this site or for a little over $100 at performance products. If you check with the parts shop here, I expect that they can sell you the same one for the same money.
Don't dare replace one without also replacing the other. Also there are two donuts on the passenger side pinion housing. You should probably replace them or at least check them while you're there. They are not so difficult and require no special tools so you can do them any time.