Y-Haplogroup E probably originated in the Near East, but most of Haplogroup E migrated back from the Near East to Africa.
E1b1b stayed above the Sahara and spread into Europe and is now the most widespread haplogroup from the Mediterranean found among European ethnicities. Rather than being an African influence on the Middle-East, E is the Middle-Eastern influence on Africa. E1b1b is observed in significant frequencies in Eurasia, particularly in South Europe and the Balkans but also in Italy, Spain, Greece and southern France, and small amounts throughout Europe to Scandinavia. Most Sub-Saharan Africans belong to subclades of E other than E1b1b, while most non-Africans who belong to haplogroup E belong to its E1b1b subclade. (Cruciani et al, Phylogeographic Analysis of Haplogroup E1b1b (E-M215) Y Chromosomes Reveals Multiple Migratory Events Within and Out Of Africa, Am. J. Hum. Genet, p. 74)