Step 1:

A positive integer is four more than the another.

Let the second integer as $\"\"$ .

Therefore first integer is $\"\"$ .

Difference of the reciprocals of two positive integers is $\"\"$ .

Thus,

$\"\"$

$\"\"$ or $\"\"$ .

Here it is needed to consider positive integer only.

Therefore, $\"\"$ .

And the first integer is $\"\"$ .

Solution:

The two positive integers are 10 and 6.