Solution

We are given that E = 2, R = 20 and T = 12. So, first, let's substitute these values.

1. AGE = 18. So, A + G + E = 18. So, A + G = 16 because E = 2.

2. ALPHA = 55. So, 2A + L + P + H = 55.

3. CONE = 48. So, C + O + N = 46.

4. DRUG = 78. So, D + U + G = 58.

5. EATER = 43. So, 2E + A + T + R = 43. So, 4 + A + 12 + 20 = 43. Therefore, A = 7.

6. EUREKA = 73. So, 2E + U + R + K + A = 73. So, 4 + U + 20 + K + 7 = 73. Therefore, U + K = 42.

7. FLIGHT = 82. So, F + L + I + G + H = 70.

8. GHEE = 37. So, G + H = 33.

9. HERTZ = 77. So, H + Z = 77 - 2 - 20 - 12. Therefore, H + Z = 43.

10. INVAR = 80. So, I + N + V = 80 - 7 - 20. So, I + N + V = 53.

11. JOULE = 57. So, J + O + U + L = 55.

12. LIGHT = 61. So, L + I + G + H = 61 - 12 = 49. But F + L + I + G + H = 70 (from No. 7). So, F + 49 = 70. Therefore, F = 21.

13. MOON = 39.

14. NOVA = 51. So, N + O + V = 51 - 7 = 44.

15. PUN = 65.

16. QUARK = 77. So, Q + U + 7 + 20 + K = 77. So, Q + U + K = 50.

17. TONGUE = 78. So, 12 + O + N + G + U + 2 = 78. So, O + N + G + U = 64.

18. TURBINE = 109. So, 12 + U + 20 + B + I + N + 2 = 109. So, U + B + I + N = 75.

19. TWO = 17. So, W + O = 5.

20. WORK = 41. So, W + O + K = 21.

21. XRAY = 42. So, X + Y = 15.

22. YARD = 60. So, Y + D = 33.

23. ZERO = 45. So, Z + O = 23.

From No. 1, A + G = 16. So, 7 + G = 16. Therefore, G = 9.

From No. 8, G + H = 33. So, H = 24.

From No. 9, H + Z = 43. So, Z = 19.

From No. 23, Z + O = 23. So, O = 4.

From No. 19, W + O = 5. So, W = 1.

From No. 20, W + O + K = 21. So, K = 16.

From No. 6, U + K = 42. So, U = 26

From No. 4, D + U + G = 58. So, D + 26 + 9 = 58. So, D = 23.

From No. 22, Y + D = 33. So, Y = 10.

From No. 21, X + Y = 15. So, X = 5.

From No. 17, O + N + G + U = 64. So, 4 + N + 9 + 26 = 64. So, N = 25.

From No. 3, C + O + N = 46. Therefore, C + 4 + 25 = 46. So, C = 17.

From No. 13, M + O + O + N = 39. So, M + 4 + 4 + 25 = 39. So, M = 6.

From No. 14, N + O + V = 44. So, 25 + 4 + V = 44. So, V = 15.

From No. 15, P + U + N = 65. So, P + 26 + 25 = 65. So, P = 14.

From No. 16, Q + U + K = 50. So, Q + 26 + 16 = 50. So, Q = 8.

From No. 2, 2A + L + P + H = 55. So, 14 + L + 14 + 24 = 55. So, L = 3.

From No. 10, I + N + V = 53. So, I + 25 + 15 = 53. So, I = 13.

From No. 11, J + O + U + L = 55. So, J + 4 + 26 + 3 = 55. So, J = 22.

From No. 18, U + B + I + N = 75. So, 26 + B + 13 + 25 = 75. So, B = 11.

So, excepting for S, we have found out the unique number for each letter. We have used all the numbers from 1 to 26, excepting for 18. Therefore, S = 18.

So, here is what we have:

1 = W, 2 = E, 3 = L, 4 = O, 5 = X, 6 = M, 7 = A, 8 = Q, 9 = G, 10 = Y, 11 = B, 12 = T, 13 = I, 14 = P, 15 = V, 16 = K, 17 = C, 18 = S, 19 = Z, 20 = R, 21 = F, 22 = J, 23 = D, 24 = H, 25 = N, and 26 = U.

Now, we have only to substitute the letters for the numbers.

This is the secret message:

A small boy swallowed some coins and was taken to a hospital. When his grandmother telephoned to ask how he was, a nurse said, "No change yet".