If a fact is in your memory, you retain it. When you consciously recall that fact, you remember it. Think of it this way: if a file is on your computer hard drive, it is 'retained' by the computer; if it is loaded into memory (RAM), it is 'remembered'.

If you're talking about recalling information in your head you can always use remember, so if in doubt use it. Retain, personally I don't use it in replace of remember. I use retain for something that you can lose but don't e.g. He managed to retain his dignity despite making some silly mistakes.

Also you can use it if a substance retains something, such as heat or water, it continues to hold or contain it: e.g This hot water bottle retains heat for 20 minutes

To explain the difference very simply -

Retain is to keep.

Remember is to recall.

Retain is much more cold and clinical, llike "the student was able to retain knowledge of skills learned during the summer vacation". 

Remember has more depth of emotion to it, like "Do you remember the time when we fell in love?" That is why song lyrics usually have the word remember and I can't think of even one song that used the word "retain".

Thank you!!