Find the missing numbers ($A$ & $B$) in the series and find the value of $B-A$.
$$51,57,63,A,75,81,B$$

Let's find the logic behind the given number series:
* $57-51=+6$
* $63-57=+6$

The series follows a constant difference pattern of $+6$.
Following this logic:

* $A=63+6=69$
* Check: $75-69=6$ (Matches)
* $81-75=6$ (Matches)
* $B=81+6=87$

Now, we need to find the value of $B-A$:

$$B-A=87-69=18$$