Resist giving employers ANY details. Your doctor certainly won't give them any, you don't have to either. I send a text or email "I'm unwell and won't be in today" and my doctor's notes all say "Diagnosis: medical condition."
Could be a throat infection ( it currently is, it's 3am and I am sick as a dawg), could be a cold, could be a broken wrist, could be depression. They aren't entitled to know.