Question 1010556
Not both "fronts".  One of them should be a different side.  Think, "two sides, adjascent".  Imagine the box is  x from left to right, y, from up to down, and z deep (from front to back).


{{{system(x^2+y^2=25,y^2+z^2=18,x^2+y^2+z^2=32)}}}


Every variable occurs as a square only.  You can treat this simply as a linear system of three equations in three unknown variables.  


I did not go further with this, but note carefully the question.  It essentially asks for {{{x^2+z^2}}}.  Look at the last equation of the system.  You can arrange this as  {{{x^2+z^2=18-y^2}}}.