retmesaĝo

Two roots you already have: reto at rank 1435, a net, and by extension the network; and mesaĝo at rank 1109, a message. Glue them and you have a network message, which is exactly what an email is. No new root, no borrowing, no -mejlo, and the word was comprehensible on first sight to every speaker who already knew the halves. This is the affix and compounding system doing the job it was designed for, on a technology that postdates Zamenhof by a century.

Retpoŝto, the other word, and when to use which. Retpoŝto is reto plus poŝto at rank 1961: net-post, the email system. The distinction the careful writers keep is that retpoŝto is the medium and retmesaĝo is the individual item, exactly as English post is the medium and a letter is the item. In practice retpoŝto gets used for both and nobody objects; but mi ricevis tri retmesaĝojn is unambiguous where mi ricevis tri retpoŝtojn makes a pedant wince. Your address is a retadreso or retpoŝtadreso, the software is a retpoŝtilo, and the verb is retpoŝti or plainly sendi retmesaĝon. The clipped retumi means to browse the web, not to write email.

The ret- prefix element is now one of the most productive in the language: retejo a website, retpaĝo a web page, retumi to go online, retamiko an online friend, retkonferenco a video call. It arrived faster than the Akademio could rule on any of it and settled by use. See Esperanto hodiaŭ for what the network did to a language whose speakers had spent a century being thinly scattered.

For the register of the message itself, which in Esperanto is friendlier and less formulaic than English business email, see letter writing and register. The short version: Kara amiko opens almost anything, Amike closes it, and the elaborate English apparatus of "I hope this finds you well" has no equivalent and is not missed.