Answer
This statement is true.
Work Step by Step
Let the first integer be $2k+1$ and let the second integer be $2m+1$ with $k>m$ --this is necessary for two odd integers. Then, subtracting, we get $(2k+1)-(2m+1) = 2k-2m = 2(k-m)$, which must be even, as 2 divides it. Therefore, the statement is proven
