Just to add:
The term a "hot pan" can be confusing.
In regards to SS,a hot pan is one that has been heated over a medium element for a sufficient amount of time that doesn't allow the ingredients to cool down the pan.Actually heating a stainless pan over high heat can cause discoloration.
What is also important is that you add the oil just before
you add your ingredients.
Having a perfectly clean pan is also paramount.For some reason people don't seem to clean SS enough leaving a film or a cloudy residue caused by insufficent scrubbing.Use steelwool if you have to,it's not going to harm the pan,and if you don't want the small scratches from doing this,then takeout is a great alternative.
So....heat a perfectly clean pan over a medium heat until
all of the pan including the outer edges of the pan are the same temp.(you'll perfect this through experience)then
add the oil and then your ingredients that have the least amount of moisture possible taking into consideration of what your cooking.
You'll eventually find cooking over easy eggs a very simple task in SS.