Here is a proof that there is always a difference at least $54$. The basic idea is to take two sets of "small" and "large" number, and prove with PHP that there is a line covered by both a large and a small number, so that there will be a big difference on this line. Take the sets $\{1, 2,..., 26\}$ and $\{80, 81,..., 100\}$. If the first one is covered by $m$ rows and $n$ columns, then $26 \leq mn \leq \frac{(m+n)^2} {4}$, so $m+n>10$ and similarly the other set is covered by more than $9$ lines, so there is a line covered by both sets, which guarantees a difference at least $80-26=54$.