Chandra's approach helps find the possible dimensions since the total area must be the sum of all the other areas. Neither side of the rectangle can be smaller than 18 since there is a square of size 18x18 included.
Now think about the edges. One corner must include the 18 going two directions. The next pieces need to be the remaining large squares because they would never fit in the middle. Two sides of the rectangle are now complete. (Note: do not put the 14 and 15 touching) How can the remaining pieces fit together? Well, 10+4 = 14, so along the side that has the 14 you need to put the 10 and the 4 square together. This fills in everything either under or next to the 18 square depending on the way you laid your boxes.
In order to equal the 14, the 10 and another box to fit the 18 + 15 edge you need 9. (14+10+9=18+15). This completes a third side to the rectangle. The remaining 8, 7, and 1 box should be clear where they fit at this point.
I am including a picture of a partial solution.