Can guessing works here?

$|A \cup B| = |A|+ |B| - |A \cap B|$ .

Since $A$ consists of $10$ more elements than set $B$ , then $|B|= |A|-10$ .

Since $7$ elements are in common to both $A$ and $B$ , then $|A \cap B|= 7$ .

Since $A$ and $B$ have $85$ unique elements $\implies |A \cup B| = 85$ .

$|A\cup B| = |A |+| B |- |A \cap B|$

$85 =| A |+ |A | -10 -7\implies 102 = 2|A| \implies |A|= 51$ .

Set $A$ has $51$ elements.

Note: $|S|=$ number of elements in a set $S$ .