The RB211-535C engine was the planned engine for the 757, but P&W claimed 8% better fuel consumption so Boeing put us under pressure to upgrade the engine.
To make the 535-E4, the 524 Core was de-staged and put into the 535 along with the snubberless, wide chord fan blades. We also used composites in the fairings, fan nose cone and thrust reversers, and as stated blended the outer duct over a pastry cutter inner duct which got the noise down a lot.
We still couldn't quite mach the fuel economy, but we had better reliability and a quieter engine.
A lot of the tech such as non heated fan nose for self de-icing and wide chord fan blades was passed back to the 524 which formed the RB211-524-D4D with the addition of FADEC.