Not natural to this native speaker. "Emilian is an English teacher" or "Emilian is the English teacher," with the emphasis on "English" when speaking (to denote the subject he teaches rather than his nationality) would be good English.
Alternatively, if you're describing a lesson that is going on at this moment, "Emilian is the teacher of the English class," again with the emphasis on "English" in spoken language.
This written translation is ambiguous. It could mean that the teacher is from England. "Emilian is a teacher of English" would not be ambiguous, even if a little more cumbersome.