Did the guest book through Airbnb? If so then you should be able to send them a message on the Airbnb message system.
Airbnb gives hosts a temporary email address, which expires after they leave, for each guest. Other than asking them, there's no way to get their real email address.
I ask guests for their personal email address all the time as I have to send them a map to my place and the coded email does not consistently attach my map. And I give them mine as well. I have told great guests who I would love to have back that the next time they want to come, they can just email me directly to book so they save the taxes and fees. Only do this after they have stayed via airbnb, never to bypass the system for their first booking with me.
No one has ever balked at giving me their personal email address after they have booked, and of course, I send them mine when asking.