Something as simple as a computer screen.
They emit light, and yet they ALSO reflection light.
Just imagine a glossy LCD that is currently showing stripes of black and white, the black parts will reflect more of the environment than the white part.
Blender emission surface does not have parameters that allows for that, I am currently simulating it by having another geometry on top to simulate glass and it seems very inefficient to do so.
The prinicple bsdf has reflection and emission. Or you can try mix shader.
It’s basically glass with emit on the inside. Since we don’t care about transparency at all, just use a fresnel to drive the color of a glossy then simply Shader Add an Emission shader to it whose color you drive with an image texture.
Hello CarlG I think you are unto something, would you mind showing the node setup ? Thanks.
Hello CarlG, when I am free from work during the weekends, I will do a comparison between this compared to having an emission layer and then just slightly on top another plane with glass shader and I will update you.
Thanks for taking the time to share your setup, it is much appreciated CarlG 
