Let's break this down step-by-step:

1. The professor initially had 10 students, and the average grade was 82.6.
2. This means that the total of all 10 grades before one was erased was: $\text{Total} = 10 \times 82.6 = 826$
3. The professor added the remaining 9 grades and got 743.

The erased grade can be found by subtracting the sum of the remaining grades (743) from the total sum (826): $\text{Erased Grade} = 826 - 743 = 83$

So, the erased grade is 83.

Would you like further explanation or details on this? Here are some related questions for practice:

1. If the average score was 85, and the total for the remaining grades was 750, what was the erased grade?
2. What if the class had 12 students, and the average grade was 80? How would that change the solution?
3. How would the calculation differ if two grades were missing instead of one?
4. If the sum of the remaining grades was 720, and the erased grade was 78, what was the original average for the class?
5. How would you calculate the total grade if the average and the number of students are known?

Tip: Remember, when dealing with averages, the total sum of all values is the product of the average and the number of elements!