There's no numeric data in curves that you can add subtract multiply or divide. You can tie one curves effect to another with an expression. Let's say your layers were called Master and Slave. To the curves property in the Slave layer add this expression:
Now below the Curves Effect add Effect>Channels>Invert
There you go. The curves have the opposite effect on the layer.
Did this work for you???
I guess I don't understand what you want to do. The screenshot of the image alone isn't much help. I'm assuming this is not what you want.
If you've applied an animated curves effect to a layer that crushed the blacks and raised the highlights (typical S curve) and you want the duplicate layer to show raised blacks and crushed highlights (inverted S) Then set up your composition like this:
The copy layer (outside the inset with the black stroke) was inverted, the curves effect duplicated and linked to the curves effect on the original, then the layer was inverted again. Here's the logic. We are not inverting the curve really, we're rotating it 180º. Kind of flipping it on it's end. The blacks are now offset the same amount in the copy that the whites were offset in the original. The S curve was not symetrical. The more symetrical the curve the closer the copy will be to the original. A perfectly symetrical curve will give exactly the same color values to both images so there will be no difference between them.
Inverting the curve will push blacks to white and white to black (make it a negative). Since that is what is happening in your sample image I am assuming that's not what you want. Try curves on one layer and simply drag the black point all the way to white and the white all the way to black. This inverted curve produces this:
I'm also confused when you said "what I got back didn't match the original image. If you just want to revert to the original don't apply curves to the copy.
I hope this helps.