First, it's not "e.i" it's "i.e."
Both "i.e." and "e.g." are from Latin and have different meanings and uses:
i.e. = "id est" which means approximately "that is [to say]"
Use it to expand further on a term or statement:
The countries of North America, i.e., Canada, the US and Mexico.
e.g. = "exempli gratia" which means approximately "for [the sake of] example"
Use it to introduce an example or examples to illustrate a term or statement:
Take a country in North America, e.g., Canada.