'Can I find a semi-transparent layer's colour and transparency using before and after values?

I have two images, one is a portion of an original image, the other is the whole of the original image covered by a uniform semi-transparent colour layer (in this case orange).

Can I use the colour difference between pixels from the first and second images to reverse engineer the colour and transparency of the covering, and if so can I then use it to find the original colour of a pixel without an uncovered equivalent? Is there just a nice single button solution within GIMP or do I need to do some actual programming/maths? I have basically no experience with image manipulation so any help would be appreciated.

Here are the uncovered and covered RGB values to help explain (and the missing value at the bottom).

Colour Base +Transparent
Colour 1 #179fb7 #f8b76f
Colour 2 #2fafc8 #f8bf6f
Colour 3 #3fc8d8 #f8c877
Colour 4 #578f08 #f8b73f
Colour 5 #6faf2f #f8bf47
Colour 6 #87c847 #f8c84f
Colour 7 #9fd85f #f8c857
Colour 8 #d0bf47 #f8bf4f
Colour 9 #8f9f1f #f8b747
Colour 10 #6faf2f #f8d077
Colour 11 ? #f8d06f

I assume you can find every possible colour-transparency pair that would cause the transformation for each row and the plot each as a line to find the intersection point, but I don't know enough about how colour works to do that.



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