What is wrong with the transmission, perhaps we can help.

They are interchangeable, but:

The 300E transmissions start in 2nd gear, extremely annoying IMO. If you can find an E320 transmission for the 1st-gear-start, or another '87 300D it would be simpler.

Also, is your torque-converter good? The torque-converter will have a different (higher) stall-speed on the 300E, not a deal-breaker but you will probably lose just a little fuel mileage.

If the valve-body is okay in your 300D, that is another option, use the 300D valve-body in the 300E transmission to retain the 1st-gear start.

If I remember the gearing is also slightly different, but 4th-gear is 1:1 (minus TC losses) on both so you'll be fine there.

Last, I'm not sure where the speedometer ratio is changed for the different diff-ratio, likely in the speedometer but I'm not sure, someone else might know if this swap will affect your speedometer.

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Gone to the dark side

- Jeff