Born in Königsberg, after attending grammar school in Gdansk, Engel studied philology at the Humboldt University of Berlin and was awarded a doctorate in 1847.
He went afterwards to the Evangelisches Gymnasium zum Grauen Kloster in Berlin as a probationary teacher.
He already learned to play the piano in Gdansk and also listened to lectures on music during his studies in Berlin.
After completing his probationary year as a teacher, he turned increasingly to the study of music theory.
In 1863, he started to teach voice at Theodor Kullak's Neue Akademie der Tonkunst and in 1874 he was appointed professor at the Universität der Künste Berlin.