To preface, Egyptian hieroglyphics are like ancient Hebrew script in the sense that only the consonants were written down; the vowels were omitted. For example, a hieroglyphic inscription would record the name "Amun-Re" as MN-R. That leaves scholars with the difficult task of supplying the missing vowels.
About a century ago, Egyptologists adopted a quasi-arbitrary vowel convention to allow them to pronounce the names of Egyptian deities and people. That's ultimately where "Ra" came from. It's a lot easier to say "Amun-Ra" than "MN-R".
However, since that time, careful comparisons with Egyptian names transcribed into other languages that did record vowels, like Greek and Assyrian, as well as comparisons with Coptic, a later phase of the ancient Egyptian language, allowed scholars to reconstruct what the vowels originally were.
For example, the last part of "MN-R" appears in Coptic as "Ρη," which is equivalent to the Greek "Re" (long "e"). But in Akkadian, it is transcribed as "Rîa."
"The Akkadian version doesn't show us the 'ayn, but it does throw in an extra "a." Such an "a," however, is a familiar phenomenon from Hebrew and Arabic. Guttural consonants are hard to pronounce at the end of words."
http://www.friesian.com/egypt.htm
You can read that link further for a more detailed description of the phonology. To give my short summary though, "Ra" and "Re" are two inexact transcriptions of the same word that have both gained acceptance. Both are acceptable transliterations in our language. In fact, the Wikipedia article on Ra/Re lists both transcriptions as equivalent names: http://en.wikipedia.org/wiki/Ra
P.S. You may be interested to know that Egyptologists have reconstructed the original pronunciation of "Amun" as Yamānu (yah-maa-nuh). It became "Amoun" in Coptic from which we get our "Amun."
http://ancientegypt.wikia.com/wiki/Amun