The product of L.C.M. and H.C.F. of two numbers is 336 and their difference is 10. Then the numbers are?

Let the two numbers be $a$ and $b$.We know that the product of two numbers is equal to the product of their LCM and HCF:
$$a\times b=\text{LCM}\times \text{HCF}=336$$
Given that their difference is 10:
$$b-a=10⟹b=a+10$$
Substitute $b$ into the product equation:
$$a(a+10)=336$$
$$a^2+10a-336=0$$
$$(a+24)(a-14)=0$$
Since numbers are positive, $a=14$.Then, $b=14+10=24$.Therefore, the numbers are 14 and 24.