Stainless Steel French

Stainless Steel French
How can I cook eggs in a stainless steel frying pan without them sticking???

I bought a $100+ Professional Stainless steel frying pan, because I was tired of oil beading up in my teflon one. I'm able to fry most things (like french toast, pancakes, etc.) without any sticking at all--just making sure the pan is hot enough and has enough oil in it. But when I cook eggs at a high temperature (i.e. I strongly feel the heat emanating from the pan when I hold my hand over it), they form a lot of bubbles on contact, almost as if they foam up, and I really need to scrape them off afterwards, leaving lots of residue that I have to take steel wool to. If I cook them at a lesser heat (using butter not oil, because at the higher heat the butter burns) the eggs become completely stuck to the pan. Does anybody have any advice please?

have the oil really really really hot. that's when you put the egg. it will cook very fast. once you see the white cooking, its ok. its done. it wont stick.