In the forrectly worked subtraction problem below, each letter represents a different digit. What is the largest possible value of E?

FLEA
- BEE
_____
MOLE

To determine the largest possible value of E, we need to find the maximum value that can be subtracted from A to obtain L.

In this subtraction problem, we are subtracting BEE from FLEA to get MOLE. Since each letter represents a different digit, we can assign values to the letters as follows:

F = ?
L = ?
E = ?
A = ?
B = ?
M = ?
O = ?
E = ?

To find the largest possible value of E, we need to consider the largest possible values for A and L.

Since A is being subtracted from something greater (F), we want to choose the largest value for A, which is 9.

For L, we need to subtract B from F, and since FLEA - BEE = MOLE, L must be one less than F. Since A is already 9, the largest possible value for F is 8. Therefore, L can be 7.

Now, let's plug in these values and calculate E:

F = 8
L = 7
E = ?
A = 9
B = ?
M = ?
O = ?
E = ?

We can subtract BEE (BEE = 100) from FLEA (FLEA = 897A) to get MOLE (MOLE = 786E). Since L = 7, the subtraction becomes:

87EA
- BEE
______
78xE

To determine the largest possible value of E, we can try different values for B, M, and O and see if the subtraction works out without repeating any digits. Starting with the largest values:

Let's assume B = 2, M = 6, and O = 3.

Subtracting 2 from 8, we get 6, leaving us with 7, 6, A, and E. Subtracting E (which is unknown) from 7 should give us E. However, we already have a 6 in the result, which means E cannot be 6 in this case.

Let's try different values for B, M, and O until we find the largest possible value of E:

If B = 1, M = 6, and O = 3, we would have:

87EA
- 1EE
_____
76xE

Now, subtracting E (which is unknown) from 7 should give us E. Since there is no digit repeated in the result (76xE), the largest possible value for E is 5.

Therefore, the largest possible value of E in this subtraction problem is 5.