Through the a Swedish forum for discussions concerning archaeology, Arkeologiforum, I found this newsflash:
Do you want to hear how the Neanderthals talked? In an article in NewScientist one can read about the research and results made by Robert McCarthy, an anthropologist at Florida Atlantic University. He has found that the Neanderthals voices were not as guttural as has been believed but more nasal and shrill. Here you can listen to McCarthy simulate an “E”.