Let [tex]x,y[/tex] be our number. Suppose [tex]x[/tex] is the largest. It exceeds [tex]y[/tex] by 19, meaning
[tex]x=y+19[/tex]
we also know that their sum is 49:
[tex]x+y=49 \iff (y+19)+y=49 \iff 2y = 30 \iff y=15[/tex]
And we deduce
[tex]x=y+19 = 15+19 = 34[/tex]
