I don’t know much about Torah im Derech Eretz, but I can explain (at least what I think based on my experience in YU) what Torah uMadda is. To be truthful, I don’t think there’s one clear definition of Torah uMadda because I think each YU Rosh Yeshivah shlita has a slightly different definition of what Torah uMadda means, but I’ll give you my opinion what I think it means.
Torah uMadda is the creed of Modern Orthodoxy (I think). Some people think Modern Orthodoxy is about being as much like the Goyim as possible while staying faithful to Halachah. I think that is completely false. I think Modern Orthodoxy/Torah uMadda, at least in its ideal form, is recognizing that while Torah is the absolute ikar, there is what to gain from secular society to enhance the Torah. There’s science, math, music, art, etc… Torah uMadda is about utilizing the positives of secular society to enhance our own Torah and relationship with HKB”H while keeping our identity as Jews (and not trying to mimic the Goyim), keeping the Torah ikar, and rejecting all that is treif in secular society. This is in contrast to the more Charedi perspective which is not to use secular society at all, whether for positive or negative (because the dangers are too great and it’s not worth the risk), unless one needs to use secular society (like for parnassah).