Professor Gutfreund confirmed the eight-page appendix of the 1930 unified theory paper had never been published, though researchers possessed copies.
The letter included a passage that Hebrew University researchers believe to be denouncing psychoanalysis founder Sigmund Freud as a fraud.
Researchers are now preserving and digitizing the new documents, after which they will work to pick through the scientific and mathematical meanings for the calculations found within their margins.
The letter begins with Albert Einstein apologizing for not answering a previous message because he was "so much in the claws of the mathematical devil that I don't get around to any personal writing at all, because I am chasing after hopeless goals that my head is good for nothing of a contemplative nature".
Most of the documents constitute handwritten mathematical calculations behind Einstein's scientific writings in the late 1940s.
According to the university, the appendix was thought to be lost.
Einstein, who developed the theory of relativity, a pillar of modern science, tried unsuccessfully for decades to prove another concept - that electromagnetism and gravity were different manifestations of a single fundamental field.
Einstein, who left Germany just before Adolf Hitler came to power in 1933, renounced his German citizenship that year.
"I believe that even in Germany things are slowly starting to change", he wrote.
"The German armament must be extremely unsafe; but the rest of Europe is now starting to finally take the thing serious, especially the English", Einstein wrote. Three letters from 1916 talk about his work on the absorption and emission of light by atoms, which would later become the basis for laser technology. In one of their letters, Einstein wrote with a touch of sarcasm that he "as a "Jewish saint" must feel ashamed at the fact that I know next to nothing of it". In one, Einstein teases Besso for having converted to Christianity, "You will certainly not go to hell, even if you had yourself baptized".
To date, Hebrew University's Albert Einstein Archives holds more than 80,000 items, including manuscripts, correspondences, photographs, diplomas and medals. "If they would have come down hard a year and a half ago, it would have been better and easier".
Einstein's more human side can be seen in the personal letters.
Cortell Reisman's grandmother, Lina Kocherthaler, was Einstein's relative.
The collection was donated by a foundation in the United States city of Chicago which purchased it from a private collector. Diana Kormos-Buchwald of the Einstein Papers Project to decipher the scientific and mathematical contexts for numerous calculations in this new collection.