If you are referring to sending a text message like a SMS to someone else via an e-mail address, then the answer is usually no. Emails is usually not meant for this kind of use, but apparently at least in the US it may be possible. Check SteveChambers answer about that.
Your confusion most likely comes from Apples messages app, that allows you to send messages (similar to Telegram) to devices without a phone number. This, however, is restricted to Apple products like Macs and iPads.
The easiest and most obvious way for you to communicate would be via email. You have to have an email address configured in an email client (the preinstalled one on iOS is fine) and from there you can send an email to the recipient. However, the recipient needs a way of accessing their email, like an email client app or through a browser.