Problem:
  F O R T Y  +  T E N  +  T E N  =  S I X T Y





Solution:
(digit 0)  2N = 0  (mod 10)
(digit 1)  2E = 0  (mod 10)   no carry from digit 0 possible
Therefore N=0 and E=5.
Then O=9 and I=1 requiring two carries. Further S=F+1.
Digit 2 no gives the equation
 R + 2T + 1 = 20 + X
The smallest digit left is 2. So X>=2 
Therefore R + 2T >= 21. As not both R and T can be 7
one of then must be larger that is 8.
We are left with some case checkings.
Case R=8:
  Then T>=6.5 that is T=7 and X=3. There are no consecutive 
  numbers left for F and S.
Case T=8:
  Then R>=5 and as 5 is in use R>=6.
  Case R=6: As X=3 there are no consecutive numbers left.
  Case R=7: As X=4 we get F=2 and S=3. The remaining digit 6 will be Y.
Therefore we get a unique solution.

 29786
   850
   850
 -----
 31486

References:

- Longley-Cook,
  New Math Puzzle Book,
  1970, p54

- Martin Gardner,
  The Magic Numbers of Dr. Matrix,
  1985
  - Chapter 1: New York
    Note: ELEVEN + TWO is an anagram of TWELVE + ONE.