I’m sorry you are ill. I hope you get better early.
I’m sorry you are ill. I hope you get better soon.
Early means ‘before the usual or expected time’ or ‘near the beginning of a period’: ‘We arrived early.’ ‘I’ll see you early in the morning.’
Soon means ‘a short time from now’ or ‘a short time after another time’: ‘I’ll see you soon.’ ‘I hope you get well soon.’
Compare:
- The train arrived early. (= before the expected time)
- The train will arrive soon. (= a short time from now)