The handwritten missive, sent in 1928 by Einstein from Berlin to a mathematician about the formalisation of the "Third Stage of the Theory of Relativity", was snapped up by an anonymous buyer for $103,700 (83,600 euros).
The letter was written during one of the "most exciting, feverish periods of Einstein's scientific career" as he worked to hammer out one of the major scientific breakthroughs of the last century, auction house Winner's said.
It included a second note jotted by Einstein on the back of the envelope refining his thinking.
Among Tuesday's other lots were letters and photographs relating to the winner of the 1921 Nobel Prize in physics that also sold for several thousand dollars.
Winner's boss Gal Wiener told AFP that the trove "reveals the complex character of the great scientist".