Answer
Required numbers are $22$ and $12$.
Work Step by Step
Let''s assume that one number is '$x$' and another is '$y$' and $x\gt y$.
Therefore according to problem-
$x+y$ = $34$ __eq.1
$x-y$ = $10$ __eq.2
Adding eq.1 and eq.2-
$x+y+x-y$ = $34+10$
i.e. $2x$ = $44$
i.e. $x$ = $\frac{44}{2}$ = $22$
Substituting for '$x$' in eq.1-
$22+y$ = $34$
i.e. $y$ = $34-22$ = $12$
Therefore the two numbers are $22$ and $12$.
