1. You have egg on your tie.
Without an article, egg is being used as a mass noun. It's quantifiable, but not countable.
It's effectively the same as saying:
You have some amount of egg on your tie.
It could be a teaspoon worth of egg material or a cup worth. (Or any other measure.)
2. You have (an / the) egg on your tie.
This means that you have a ...