[eluser]Monarobase[/eluser]
I haven't tried this yet but this is what I have understood :
1) Get a clean copy of an application folder from the same CI version as uses Expression Engine (I haven't looked yet to make sure if it's the latest version of CI the EE uses or not).
2) Name this folder after your app and place it along side the expressionengine folder.
3) Copy the index.php file from CI to where I want the application to be (I would probably create a directory a put it in it or something similar, and I edit it so it uses the right application folder.
This is all theoretical as I have not tried it yet but if someone else who has done this before could confirm or correct these instructions it would be great !