, 2014

Solution:
Answer: 201
We know that 2014 does not qualify the property. So, we'll consider $\{4,9,14, \ldots, 2009\}$ instead. Now, we partition this set into 2 sets: $\{4,14,24, \ldots, 2004\}$ and $\{9,19,29, \ldots, 2009\}$.

For each, the first and second set are basically $x4$ and $x9$, where $x = 0, 1, 2, \ldots, 200$, respectively. And we know that for each value of $x$, $x$ must be either even or odd, which makes exactly one of $\{x4, x9\}$ have even sum of decimal digits. Therefore, there are in total 201 such numbers.