How is CODE-E a prequel of MISSION-E?
Some amount of time has passed after "CODE-E". The main change in the background story is that they've discovered that there are other people like Chinami, or other TYPE-E's in the world. This discovery (prompted by events from "CODE-E") lead to discrimination and persecution of TYPE-E's. This lead to Chinami, her friends, and some of the people she had confrontations with from CODE-E forming an organization called "OZ" which tries to help other people with the same abilities as Chinami, or other TYPE-E's. And that's where the story starts in MISSION-E.

There is an ongoing manga called "CODE-EX" and a light novel series also called "CODE-E" (which, I believe, was an adaptation of the anime series), but I'm not sure how much they fill in the missing time between the "CODE-E" and "MISSION-E" anime.