This article explains how to search for someone's email address to add them as a friend on Facebook. Instructions apply to Facebook in a web browser and the Facebook app.
2 Ways to Find Someone on Facebook Using Email
If you want to add someone on Facebook, the best thing to do is search for that person's email address.
Go to Facebook.com in a web browser or open the app on your mobile device and log in to your Facebook account if necessary.
On the web, type (or copy and paste) the email address of the person you want to find into the Facebook search field at the top of any Facebook page and press the Enter or Return key.