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... show more 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?
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