You didn't mention what model of Dometic thermostat you have, so some of this may not apply. Download the manual for your model thermostat here
Various other responses to an E4
error suggests it could be:
Out of range value for outside temperature sensor. Probably only true if you have a heat pump rooftop A/C unit)
Here's a list of Dometic Thermostat codes:
Not sure if this is the same for all models.
Press the “+” button and, while holding it, also press and hold
the On/Off Mode button for three seconds. LCD will show
? ? . Press the On/Off Mode button again to turn system off.
This completes the initialization.
Again, not sure if this is for all models of thermostat.
Another suggestion was to pull the fuse for the furnace in the house panel, wait 30 seconds or so, then replace fuse. This is also a 'reset' method.