Is a resignation and acceptance of resignation via email legal?

I submitted my 2 weeks notice to my manager via email due to a mandatory shift change that my employer knew would cause a transportation issue. My manager replied via email that she needed to confirm my actual last day, as I had not put an actual date. During this time, the schedule conflict was resolved, so I replied to the email asking for confirmation stating I wished to rescind my resignation. This all happened within less than 24 hrs from my initial email, yet my manager replied that my resignation had already been accepted (although a date was never confirmed) and could not be rescinded. This was also all done through email, with nothing ever being physically signed by myself or by HR. Is this legal?