I have been experimenting with this problem for a while now, and it can be solved, both mathematically, as well as experimentally, although the outcome in both situations is fuzzy on my end.
In both setups I have set the background or base layer as the colour to be calculated, while my overlay is your background color.
The blend mode used for this example is soft light, and following the formula given for soft light blend mode colour calculation here
you can calculate your rgb values for each value (formula taken from here), where a is the base layer value, and b is the overlay layer value. In your case, b is the unfused colour, a is unknown, the fused colour is the mathematical result of the formula, which is known.
Also, the overlay colour layer is set to soft light blend mode, just to clarify that again, because it is reversed compared to your example setup.
To calculate each value, you would express each value as divided by 255.
Look at the following example for calculating the a value for red of the base layer:
Since b is ≥ 0.5 (b = 208/255), I have used the lower formula of the split formula.
This solved for a gives us
or roundabout 245. This is the red value of the overlay.
Continuing for green and blue below.
Calculating for a’s green value gives us this
which solved for a gives us
or roundabout 172. This is the green value of the overlay.
For the blue value, we need to use the upper formula as defined above, because 71/255 is < 0.5, which leads us to this:
which solved for a gives us the final value of our overlay colour, blue as
or roundabout 106.
And here it breaks down, because the calculated values for the overlay colour is noticeably off, although I can’t say where the fault lies: my calculated colour for the overlay is 245 172 106 or #f5ac6a, following the above formula.
On the other hand, through experimentation, I have found that the colour values of 248 174 87 or #f8ae57 are much closer to the example provided. I assume that further calculation, using the other two overlay & resulting colour pairs will provide more precision through averaging all three, for instance, but in theory calculating the one should be enough, provided it is one colour with one singular opacity of 1, like Zach Saucier has mentioned in the comments.