At a low Mass (Missa Lecta) and a sung High Mass (Missa Cantata) the priest says or chants the Ite Missa est, respectively. However, at a Solemn High Mass I am reasonably certain that the celebrant (the main priest - most Solemn High Masses these days have three priests as ministers: the celebrant, deacon and subdeacon) does not chant the Ite Missa est.
ELS is correct. After Solemn Mass the Ite is chanted by the deacon. Though Mrs. Romulus and I were blessed to have a Solemn Mass for our nuptials, I confess I didn’t recall whether the Ite is sung in that form — so I’ve just dashed out to the car to check my copy of Fortescue. The answer is yes, it is chanted.
You are right, and I was wrong. Guess I don’t know much about a Solemn High Mass.