Supersonic electric flight could be a propeled glider that goes stright up, hides the propellers and engines bhind some aerodynamic covers and glides at supersonic speed, then repeats the procedure as many times as needed.
Another idea is to make a turbo-jet engine heated by electricity instead of fuel.
I guess it could depend on your definition of "glide", but I doubt that anything gliding at supersonic speed would have a very good glide ratio. Thus, it wouldn't really cover much ground even thought it might travel quite a bit vertically.
If we consider the reason one wants to travel at supersonic speeds, we might arrive at something involving the value of a human's time. Given that, slow but ultra efficient, luxurious (and internet-connected - "workable") travel might be something. Then gliding, floating, etc. with ample space and creature comforts could be the focus.
Electric jet engine powered by a heat pump. I wonder if anyone has looked into that?
You could collect a lot of heat from the airflow over the body. Meaning there would be a lot of air with some level of heat that’s constantly being replaced.
Another idea is to make a turbo-jet engine heated by electricity instead of fuel.