SOLUTION: Suppose you have a data set of 83, 84, 86, 89, 90, 92, and 92. What 2 numbers could add to the data set so that the mean is 87 and the median is 90?

83, 84, 86, 89, 90, 92, 92

If we add two more numbers to that list, there
will be 9 numbers in the list.  When there are
an odd number of numbers the median is always
the middle number when arranged smallest to
largest.  With 9 numbers the middle one is the
5th.  90 is already the 5th number, so both
the numbers we add must be 90 or more than 90,
otherwise the 90 could not be the 5th,
or, middle number.

The sum of those 7 numbers is 616.

In order for the mean to be 87 after adding two
numbers to the list, the sum of all 9 numbers
must be 87×9 or 783.

Therefore the sum of the two numbers we add to
the list must be 783-616 or 167.  

But we cannot add two numbers each of which must
be 90 or more, and yet their sum be only 167.

So what you're asking is clearly impossible. 

Edwin