Reverse Cipher Puzzle - Part 2

Looking at the formulae, you can see that in the subtraction we have, in the rightmost column, S - S = R, so R = 0 (zero). Going to the complex formula, you can see that subtracting O from TO gives a multiple of 10, so ignoring whatever T might be for the moment, (E + S) = 10. If you look at the addition, in the rightmost column, (S + O) = U (+ 10) (that is possibly 10). In the next column we have E + S, which we know is 10, so J is either zero or 1. It can't be zero because that's R, so it must be 1.

1	2	3	4	5	6	7	8	9	0
J									R

Looking at the subtraction again, we've got another formula, (E - S) = T, the second column from the right. Using what we already know about E and S, we can say:

E - S = T

E - (10 - E) = T

2E - 10 = T

2E = T + 10

E = (T + 10) / 2

So for E to be a whole number, and a single digit, T must be even.

T	E	S
2	6	4
4	7	3
6	8	2
8	9	1

T can't be 8 as S can't be 1 (it's J). In the subtraction, the third column from the right has T + E + 1 = U (+ 10), the 1 being carried over from (E + S). Plugging this into the table we get:

T	E	S	U
2	6	4	9
4	7	3	12 (or 2 + 10)
6	8	2	15 (or 5 + 10)

Remember the first formula, (S + O) = U + 10, we got from the subtraction? We substitute 10 = (E + S) as before:

S + O = U + 10

S + O = U + S + E

(removing S each side)

O = U + E

Using this to get values for O:

T	E	S	U	O
2	6	4	9	(6 + 9) = 15
4	7	3	2	(2 + 7) = 9
6	8	2	5	(5 + 8) = 13

O must be a single digit, so it can't be 15 or 13, leaving us with:

1	2	3	4	5	6	7	8	9	0
J	U	S	T			E		O	R

Putting what we know into the addition, we get 374473 + 73F739 = 1113212 and making the obvious subtraction, 1113212 - 374473 = 738739, gives F = 8, leaving C and I.

Doing the same to the subtraction, 74873 - IC233 = 18C40, the third column from the right, 8 - 2 = 6, so C = 6 and I is 5:

1	2	3	4	5	6	7	8	9	0
J	U	S	T	I	C	E	F	O	R

Which makes our formulae:

47737 * 65 = 3102905	374473 + 738739 = 1113212
74873 - 56233 = 18640	((7 + 3) * 4) + 9 = 49