#### Answer

The numbers are 19 and 45.

#### Work Step by Step

step 1
Let x represent the smaller number in the problem.
step 2
"the other number exceeds x by 26" = $(x+26)$
"Their sum" = $x+ (x+26)$
step 3
"... equals 64" is written as " = 64".
The equation is
$x+ (x+26) =64$
step 4
Solve, answer the question.
$x+ (x+26) =64\quad$. simplify the LHS
$2x+26=64\qquad/-26$
$2x=38\qquad/\div 2$
$x=19$
The smaller number is 19.
The other number is 19+26=45
step 5
Check the solution in the original wording of the problem.
45 exceeds 19 by 26. (OK)
The sum of 19 and 45 is 64. (OK)