Basically:
sf::BlendMode customBlendMode = ...;
window.draw(background);
window.draw(mask, customBlendMode);
This approach is of course limited, but it is able to lighten/darken a constant area. You may not even need custom blend modes if you simply want to darken an existing image.
More is explained in the tutorials and documentation about rendering sprites and blend modes, please read them.
Lighting systems have already been provided as an SFML extension, search for "Let There Be Light" and "GLLight2D" in the project forum.