Modifiing my previous answer thanks to you comment, I realized I not clear at all. Here it's better.
First, I want to state that the notations in your material seem weird to me as the normalizing and adimentionnality of the values are not properly presented. For the eq. 1 and 2, $T_{eq}$ and $S_{eq}$ are said to be dimensionless yet they are added to $\Delta T$ and $\Delta S$ that are not introduced as dimensionless.
In any case, it seems akin to the density anomaly (see THIS LINK, page 6). The same pdf file the link leads to bears a thorough explanation of the model (page 9 and following).
Without going trough the nondimensionalization process, by taking the density equation of salty waters, $\rho=\rho_0(1-\alpha T+\beta S)$ (increases with increasing S and decreases with increasing T with rate respectively $\alpha$ and $\beta$), you have that \begin{align}\Delta \rho&=\rho_{A}-\rho_{B}\\&=\rho_0(1-\alpha T_{A}+\beta S_{A})-\rho_0(1-\alpha T_{B}+\beta S_{B})\\&=\rho_0(-\alpha \Delta T+\beta \Delta S).\end{align} Using $R=\frac{\beta}{\alpha}$ and $\Delta \rho_*=\frac{\Delta \rho}{\alpha\rho_0}$ leads to $$\Delta\rho_*=-\Delta T+R\Delta S.$$ I'm not sure about why the absolute value is introduced, maybe because the textbook authors weren't interested in wich part of the ocean was the most dense?
You can take a look at the original paper by Stommel at he following LINK.
