Answer
$T\Delta S$ is positive and greater than $\Delta H$.
Work Step by Step
If $NH_4NO_3(s)$ dissolves spontaneously in water, $\Delta G=\Delta H-T\Delta S$. Basic properties of mathematics tell is that if $ \Delta G$ is negative and $\Delta H$ is positive then $T\Delta S$ must be positive and greater than $\Delta H$.
