[tex]\displaystyle \\
\overline{xy} - \overline{yx} = 45 \\ \\
10x+y - (10y+x) = 45 \\ \\
10x+y - 10y-x = 45 \\ \\
10x - x +y - 10y = 45 \\ \\
9x -9y = 45\\\\
9(x-y)=45\\\\
x-y= \frac{45}{9} \\ \\
\boxed{x-y = 5}\\\\
\text{Solutii: }\\\\
x=9~si~y = 4\\
x=8~si~y = 3\\
x=7~si~y = 2\\
x=6~si~y = 1\\\\
\Longrightarrow~~\overline{xy} \in \{94;~83;~72;~61\}\\\\
\text{Verificare: } \\
94 - 49 = 45 \\
83-38 = 45\\
72-27=45\\
61-16 = 45
[/tex]