The paper is behind a paywall, so I haven't seen it. You can contact the author for a copy. Nevertheless, the derivation is straightforward algebra from a pair of simultaneous equations based on the Beer-Lambert law.

Consider that the absorbance (A) at each wavelength (280 for the protein and D for the drug) is made up of 2 parts, the absorbance of the protein (p) and the absorbance of the drug (d).

A280 = A280(p) + A280(d)

AD = AD(p) + AD(d)

Each of these absorbances equals the concentration (C) of the absorber times the extinction coefficient of the absorber (E) at that wavelength, according to the Beer-Lambert law, where the pathlength is not shown because it is held constant: A = CE (I'm avoiding Greek letters.)

The idea is that you will have measured the absorbance spectra of the protein and the drug separately, so you will know the values of the extinction coefficients at both wavelengths for both substances, a total of 4 extinction coefficients. There are only 2 concentrations, that of the protein (C(p)) and that of the drug (C(d)), which are what you want to know.

A280(p) = E280(p)C(p)

A280(d) = E280(d)C(d)

AD(p) = ED(p)C(p)

AD(d) = ED(d)C(d)

Note that there are 2 unknowns, C(p) and C(d), so we need 2 equations. Everything else is either a constant (E) or a measurement (A).

Substitute the ECs into the equations at the top.

A280 = E280(p)C(p) + E280(d)C(d)

AD = ED(p)C(p) + ED(d)C(d)

Pick either C(d) or C(p) to solve for, it doesn't matter which.

C(d) = [A280 - E280(p)C(p)]/E280(d)

Substitute this expression for C(d) into the other equation and solve for C(p).

AD = ED(p)C(p) + ED(d)[A280 - E280(p)C(p)]/E280(d)

AD = ED(p)C(p) + ED(d)A280/E280(d) - ED(d)E280(p)C(p)/E280(d)

AD - ED(d)A280/E280(d) = ED(p)C(p) - ED(d)E280(p)C(p)/E280(d)

AD - ED(d)A280/E280(d) = [ED(p) - ED(d)E280(p)/E280(d)]C(p)

C(p) = [AD - ED(d)A280/E280(d)]/[ED(p) - ED(d)E280(p)/E280(d)]

C(p) = {[ADE280(d) - ED(d)A280]/E280(d)}/

{[ED(p)E280(d) - ED(d)E280(p)]/E280(d)}

C(p) = [ADE280(d) - ED(d)A280]/[ED(p)E280(d) - ED(d)E280(p)]

(Multiply by (-1)/(-1) to get the expression in the picture.)

Repeat for C(p) to get C(d).

Please try to approach to author.

Thanks for your kind helps