What is the difference in meaning between Elohim and Elohe?
The former is "God", the latter is "God of", such as "God of Abraham" (Elohe Avraham)
The latter is from the grammatical construct called סמיכות which is a way of connecting noun-noun pairs. In english, we use "of", but in hebrew there are quite a few ways of doing this. של is usually used in place of "of" in hebrew, but in this case, we modify the first word, with the suffix "ey" (which is what we do for plural words, which God's name is in Torah), so it becomes Elohei Avraham.