There's allergies, and there are food intolerances, two different but related things. IGE is used to measure food allergens while IGA is used to measure food intolerances. They both cause an immune system reaction, but one can result in allergy like symptoms like an insect bite, while the other is delayed and often results in gastro-intestinal symptoms (and sometimes neurological symptoms).

You can have either or both at the same time.