#### Answer

The numbers are $17$ and $41$.

#### Work Step by Step

step 1
Let x represent the smaller number in the problem.
step 2
"the other number exceeds x by $24$" = $(x+24)$
"Their sum" = $x+ (x+24)$
step 3
".. equals $58$" is written as " = $58$".
The equation is
$x+ (x+24) =58$
step 4
Solve, answer the question.
$x+ (x+24) =58 \qquad$ ...simplify the LHS
$2x+24=58\qquad/-26$
$2x=34\qquad/\div 2$
$x=17$
The smaller number is 17.
The other number is $17+24=41.$
step 5
Check the solution in the original wording of the problem.
$41$ exceeds $17$ by $24$. (OK)
The sum of $17$ and $41$ is $58$. (OK)