The brief
The E250 squealed for the first minute on a cold start, then quieted once warm. With the engine off, the auxiliary belt showed obvious cracking and a shiny, glazed surface. Two related parts at the end of their life.
The auxiliary belt, the long ribbed belt, drives the alternator, the air-con compressor and the other accessories off the crankshaft. It runs over a tensioner that keeps it tight. A belt that has glazed slips on a cold pulley until friction warms it up, which is the squeal that fades, and a tensioner that has lost its spring lets it slip in the first place.
The diagnosis
The belt was past replaceable wear, cracked and glazed. The tensioner pulley had visible bearing roughness when spun by hand, and its spring tension measured below spec, which is why the belt was slipping when cold.
Doing one without the other makes no sense, a new belt over a weak tensioner just slips again. So the fix was both, replaced as a set.
The work
The belt routing was marked, the tensioner released, and the cracked belt removed. The failed tensioner came off its mount, a new Mercedes-spec tensioner went on, the new belt was routed, and the tensioner released back to working tension.
The engine was run to confirm clean, quiet operation with no slip before the car went back to the owner.
The outcome
No squeal at cold start, the belt running quietly, and the tensioner holding spec under load.
The E250 went home with the accessory drive sorted. For the owner that is a quiet engine again, and doing the belt and tensioner together means the accessory drive is fresh as a set rather than the tensioner being the next thing to fail.