jmc

We can group each subtracting pair together: $$(100-98)+(96-94)+(92-90)+\dots +(8-6)+(4-2).$$ After subtracting, we have: $$2+2+2+\dots +2+2=2(1+1+1+\dots +1+1).$$ There are $50$ even numbers, therefore there are $\frac{50}{2}=25$ even pairs. Therefore the sum is $2\cdot 25=\boxed{50}$