As per given by the question,
There are given that the sum of two number is -8 and their dufferences is 44.
Now,
Let the two number is, x and y
Then,
The sum of two number is -8.
So,
![x+y=-8\ldots..(1)](https://img.qammunity.org/2023/formulas/mathematics/college/7oi5zeynrgw658vp5y1u9citj85l6m5lte.png)
And,
Their differences is 44.
So,
![x-y=44\ldots(2)](https://img.qammunity.org/2023/formulas/mathematics/college/7l0e65r4awfc3z7n8tpvhsoho4xvmfirhl.png)
Now,
For find the value of two number, x and y
From equation (2)
![\begin{gathered} x-y=44 \\ x=44+y\ldots(3) \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/xk1lwpakx7k9iahb9wv8kwip9q1sn2fxxn.png)
Put the above value of x into the equation (1).
So,
![\begin{gathered} x+y=-8 \\ 44+y=-8 \\ 44+y-44=-8-44 \\ y=-52 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/emm3s5ah8566xen4xnzzcbhn06byp9hrgb.png)
Now,
Put the value of y into the equation (2)
So,
![\begin{gathered} x-y=44 \\ x-(-52)=44 \\ x+52=44 \\ x=44-52 \\ x=-8 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/n2tx7tpdpz0w9f9d1bz01sa4ask6h7njvg.png)
Hence, the number is shown below:
![x=-8\text{ and y=-52}](https://img.qammunity.org/2023/formulas/mathematics/college/gp5jjxm3rlt5p8vja775oa3dt54htpe6tl.png)