Power Circuit to Subtract a Voltage by a Known Amount
I know subtracting voltages can be done with OpAmps, but I'm specifically looking to do this and draw a measurable amount of power from the output (> 50mA). The best solution I could conjure to date involves a transformer.


Yet you're so close with the opamp: 

Imagine this: you've got a component that acts as a resistor, but is always automatically set to a resistance that leads to exactly the voltage drop you want.

If you know the voltage from which you're subtracting (e.g. it's always 10V), then a simple linear (positive) voltage regulator would do. 

You can build such a dedicated voltage dropper (it's simply a linear regulator, by the way, but not in its most common positive-voltage-relative-to-ground variant).

Something like (doing this from the top of my head, so add additional components for stabilization and what not if this doesn't perform well enough):







simulate this circuit &ndash; Schematic created using CircuitLab