$\displaystyle{\left|-{23}\frac{{7}}{{8}}\right|}-{\left|{10}\frac{{3}}{{4}}\right|}={23}\frac{{7}}{{8}}-{10}\frac{{3}}{{4}}={23}\frac{{7}}{{8}}-{10}\frac{{6}}{{8}}={13}\frac{{1}}{{8}}\usepackage{cmbright}\Huge\$

The number with the greater absolute value is negative, so the sum is negative.