When you enter the game for the first time, you will need to register with a Facebook account or an email address to start playing.
The game information such as statistics and purchases will be associated with the account. This is why you can't change the email address, since all of your achievements would be lost.
Bear in mind that if you create the account with an email address, you'll still be able to link it to a Facebook account later. To do so, go to Options > Account > Facebook and select 'Link'.
You'll also be able to unlink it later. To do so, there must be an active email address associated with the game account.