Solve Two-Digit Addition: 23 + 59 Using Column Method

To solve this problem, we'll use vertical addition and work through each step:

Consider the numbers:

$\begin{aligned} &23 \\ +& \\ &59 \\ &\underline{\phantom{776}} \end{aligned}$

Step 1: Align the numbers by their place values.
Step 2: Add the units place: $3 + 9 = 12$. Here, $12$ has two digits. We place $2$ in the units column and carry over $1$ to the tens column.
Step 3: Add the tens place along with the carry: $2 + 5 + 1 = 8$. Place $8$ in the tens column.

The final sum will be as follows:

$\begin{aligned} &23 \\ +& \\ &59 \\ &\underline{\phantom{776}} \\ &82 \end{aligned}$

Through these steps, we find that the sum of the numbers $23$ and $59$ is $82$.

Therefore, the solution to the problem is $82$.