interfacing to PWM motor controller

This controller output is set using a potmeter:

it's power specs perfectly suited for my purpose (driving a solenoid with 24 volt, max 20 amp)

I only don't know how to interface this unit with the arduino.

Is it even possible? if so how would you do this?

The module is designed to take a potentiometer as the control input. You would need to reverse engineer the pot input circuitry before deciding if it is even possible to interface with Arduino.

Looking at the board photo, my guess is that the pot controls the pulse width of an on board oscillator, like a 555 timer. If so, you might be able to remove the timer chip and create an Arduino interface using an optocoupler.