No, sorry but I can not. If the person sending didn’t add their e-mail to the back of their card I will assume they choose not to do that. Maybe they’re not comfortable sharing it. So I will not give out their e-mail to you.
Send them a silent thank you in your head, that will be enough.
One of the things I love about sending real art through the mail system is to get away from e-mail for a while, so I don’t think anyone needs to e-mail their gratitude at all. But it’s up to you, and if you get an e-mail address on your postcards, it’s up to you if you want to contact the sender or not.