The blower housing has decal information: "B&S 500E Series"/140cc I could never find a specific model information for just the engine on the engine proper. FYI, I could not find in the MTD website specific mower model differentiation by a specific B & S engine model.
The old starter, in pieces, did not include a separate ring that fit the starter bolt hole pattern. It to looks like it snaps in the blower housing from the inside. There were no washers or spacers that might lift the starter and housing to prevent the binding.