generating a -10v...+10v control signal from an arduino

anyone got a better grasp of technical german??

No but if you scroll down the data sheet the bottom half is repeated in English! :wink:

So yes it is a differential input. That means the two signals both go from 0 to 10V, it is just that when one is up and the other is down that is a 10V signal but when this is reversed it is a -10V input. But there is not a -10V with respect to ground it is just with respect to the other signal.
Therefore you need two 0 to 10V analogue signals. I would put the PWM first through a transistor to get it in the 0 to 10V range, and then filter it to remove the PWM switching noise. This is simpler than smoothing it and then having to get a linear amplifier to boost it up to 10V.