Here's why:
* Stress: The word "entrance" has stress on the second syllable ("trance").
* Unstressed vowels: Unstressed vowels often have a reduced sound, sometimes sounding like a schwa (ə). In "entrance", the first syllable is unstressed, making the "e" sound more like a schwa.
So, while we spell it "e", it's pronounced more like a short, almost silent sound.