Let we have two vectors are a and b

We add these vectors as: a + b

and subtract these two vectors as: a - b                  

Now, a - b = a + (-b)

Thus to subtract b form a, reverse the direction of b and add to a.

So, there is no such condition.

Again if |a - b| = |a + b|, the vectors a and b are perpendicular to each other.