You can, but only programs on the homescreen written in TI-BASIC. This means probably most math programs and a few simple games, however unfortunately you won't be able to get things like Mario or Fruit Ninja on a CE - as they are written in assembly (specifically for the 84+). I think that maybe some programs would work on the graphscreen, just the images would be all messed up as any text placement would be messed up.
To add to what DWMelon said, pure TI-BASIC games written for the TI-84+CSE (or CSE as it's referred to) will generally work with the CE.
Again adding on, "pure TI-BASIC" means it does not depend on any Basic hybrid libraries, such as xLIB.
Basically that means if it requires Doors or another library, it won't run on the CE. Although it might copy over.
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