As David said, this looks like window light with a reflector or a softbox with reflector.

The whole portrait lighting from what I learned thirty years ago was essentially Rembrandt lighting. This is using a north window light ( because it is never direct light) and a reflector of some sort. (fomecore works fine) The whole softbox thing evolved from that to duplicate the look.

To do the same type of lighting as your example you need a camera with a lens that has the ability to move in this close and window light with a reflector. Thats it. If not then a softbox real close and a reflector.

Sometimes when I shot on location or weddings, the person had shear drapes in their home that gave the same type of light as a softbox. Obviously then you don't need a north window just as long as there isn't direct sun coming though.

I would just take your camera, position the person in front of the light source and move them around until you got what you liked. If you are using a window/softbox, then you can see the light pattern and when you get what you like, add the reflector to control the contrast.

It is a very simple form of lighting.

Michael McBlane