No, it isn’t possible.

The Era's have bluetooth, but are meant to receive, not transmit.

Even if you could, I’m not sure what is meant by “listen to the Era 100 or 300 through headphones”.  Certainly the headphones have their own speakers, so the Era speakers would be bypassed by the headphones and you would not be listening “through” the Era speakers, they would be silent. 

There are only two Sonos products that have any sort of audio output that can be used by 3rd party hardware.  The port is one, which has RCA and Coax output, which could be used by wired headphones or wireless via a bluetooth transmitter.  The other is the Amp, which has left and right speaker level outputs for passive speakers.  That would be challenging to get that audio to headphones, but it could be done.