Could someone suggest for me a text explaining in details the mathematics behind LIMMA when we have a quantitative outcome. Most of the available literature I have come across explain LIMMA mathematically when  we have two- sample groups. For example, instead of using D=mean(x)-mean(y), do we use regression coefficient when using quantitative outcome?

Thank you in advance . 

It's just conventional linear regression. The coefficients you end up estimating are interpreted as the change in gene expression for a unit change in your continuous variable. There are slight differences (you might fit a weighted model, and the standard errors and denominator degrees of freedom are slightly different than what you normally compute), but in general you would just be fitting a regular old linear regression.