Historians haven't been able to find an account of the Exodus in Egyptian records. That's because they were looking in the wrong time period. Currently, the majority guess places it in the time of Ramses II, a strong, stable society unlikely to allow the escape of a horde of slaves.
There is an existing description of the Plagues, however, by an Egyptian eyewitness. The Ipuwer Papyrus describes the same plagues as the Bible does. Ipuwer wrote his account at the end of the Middle Kingdom, a time which included the death of their pharaoh by drowning, followed by their conquest by the Hyksos and the Egyptian Dark Ages. The difference in time between this point and the currently popular guess is about six centuries. By the time Egypt has surviving written records again, it is possible to lay those records alongside the Palestinian-Syrian histories, shift them six centuries, and match up the wars, diplomacy, and cultural styles.
No one has been able to do more than guess at who was the King of Punt visited by Pharaoh Hatshepsut. No one has been able to more than guess at who was the Queen of Sheba who visited King Solomon. That's because they seemed to be six centuries apart. The records of these two visits show the same events and the same gifts exchanged.
The el-Amarna letters, a cache of diplomatic correspondence found in Ahknaton's abandoned capitol, describe events in Syria-Palestine that no one had been able to match up. Shift them six centuries, and they match the events described in the Books of Kings and Chronicles, the Mesha Stele of Moab, and Assyrian records.
Funerary styles and styles of jewelry disappear for six centuries and then reappear in another place. Styles of written records do the same. Based on those written record styles, philologists were forced to theorize an entire people whose existence couldn't be found by archaeologists.
The culprit in all this is Egyptian star dating. Velikovsky, a genius on the level of Einstein – in fact, the two were friends – added an appendix to his final book of historical revision, exposing the guesswork on which Egyptian star dating was based. With all those lovely star maps on the walls they found, Egyptologists just had to use them, so they took a stab at an unidentifiable proper name and stated firmly that this guessed identification had to be the time that matched the maps. The resulting wild stretches of explanation become unnecessary when star dating is tossed out and the normal comparisons of culture and historical events are used.