I'm not sure this applies here. Equal temperament explains how an interval is in tune and does not determine what key a song is in.

Torrent-of-ions is correct. Equal temperament is a compromise in tuning (assigning pitches to notes) which makes the most keys sound ok. The intervals aren't perfect, but close enough. If you tuned a piano for perfect intervals in one key, those pitches would be too much off for another key.

See e.g. http://www.phy.mtu.edu/~suits/scales.html

Yes, equal temperament is basically a compromise of tuning methods. While it can help ensure that a piece which modulates into different keys is in tune (as close as possible), equal temperament cannot tell the key that is being played.