Complete the squares so that the differences shown on the outside are correct

We have that the Number to complete the missing squares are

From the question we are told that:

Within the Box 1 =8 and 2

Outside box 2= 1,3,5,3 Respectively

Within the Box 2 =8 and 9

Outside box 2= 19,6,7,10 Respectively

Let

x and x' be the top missing squares for Respective Boxes

y and y' be the bottom missing squares for Respective Boxes

Differences

Differences in   mathematically is simply using the minus operator between two or more numbers

Therefore

For Box 1

The first space is we are tasked to find a number x where

The Second space is we are tasked to find a number y where

For x

For y

For Box 2

The Second space is we are tasked to find a number y where

The Second space is we are tasked to find a number y where

For x'

For y

In conclusion

The Number to complete the missing squares are

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8 5                   and 18 8

7 2                           9 2

8 - 5 = 3, 8 - 7 = 1, 5 - 2 = 3 and 18 - 8 = 10, 18 - 9 = 9, 9 - 2 = 7, 8 - 2 = 6