Tôt is wrong to say you are early today? Why?
Tôt is early in a general sense. En avance is early with respect to a specific time, i.e. "ahead of time".
Tu t'es levé tôt ce matin. -- You got up early this morning.Tu t'es levé 10 minutes en avance. -- You got up 10 minutes early.
Often, there is an implied time something ought to have happened. In the second sentence above, the implication is that there was some kind of expectation that you usually get up at a specific time, but this morning you got up 10 minutes earlier than that. It could be that you usually get up at 10 am and today you got up at 9:50 am. That isn't particularly early (tôt) but it is earlier (en avance) than expected.
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