This is your personal matter. Whether you want to discuss it with the fellow teachers or students depends on your circumstances, work envoirnment and relationship with the school staff/students. If you feel there is no harm to anyone and you want to share the news (people will take it positively), go ahead.
However, in most cases I have seen people don't share details and simply state that they were not feeling well and needed a break (this is not a lie).