In essence, a solemnity is as important as a Sunday, and Sundays are never days of fasting or abstinence. (See "Should We Fast on Sundays?" for more details.) That is why the Code of Canon Law (Can. 1251) declares:
Abstinence from meat, or from some other food as determined by the Episcopal Conference, is to be observed on all Fridays, unless a solemnity should fall on a Friday [emphasis mine].
There are two solemnities that can fall during Lent: the Annunciation of the Lord and Saint Joseph's Day. Whenever either of these solemnities falls on a Friday, the faithful are dispensed from the requirement to abstain from meat.
You may have noted as well that Canon 1251 doesn't single out Fridays in Lent but says that "Abstinence . . . is to be observed on all Fridays" (emphasis mine). Many Catholics do not realize that the Catholic Church still requires Catholics to abstain on all Fridays of the year, either from meat or from some other good thing (as determined by each country's national conference of bishops). For more details, see Abstinence as Spiritual Discipline.