#### Answer

$x=19$
$y=45$

#### Work Step by Step

Step 1. Let $x$ and $y$ be the two numbers.
$x$ = the first number
$y$ = the second number
Step 2. Represent other unknown quantities in terms of the other.
Hence, the phrase, "One number exceeds another by 26" --> $x+26=y$
The sum of the numbers is 64 --> $x+y=64$
Step 3. Write the equations that model the conditions.
$x+26=y$ -->equation 1
$x+y=64$ -->equation 2
Step 4. Solve the equation and answer the question.
Substitute equation 1 to equation 2:
$x+(x+26)=64$
$x+x+26=64$
$2x+26=64$
Subtract 26 to both sides:
$2x+26-26=64-26$
$2x=38$
$x=19$
Substitute to equation 1:
$x+26=y$
$19+26=y$
$y=45$
Step 5. Check the proposed solution in the original wording of the problem.
Use equation 2:
$x+y=64$
$19+45 = 64$
$64=64$ --> TRUE