Answer


T = 1
L = 4
A = 6
H = 9

E = 2
R = 8
T = 1


Check


    9641
+   9641
-----------
   19282

   Looking into the first "T" in in the sum "THERE", you conclude that T= 1.  
   It can not be nothing else.

   Then looking into last "E" in the sum "THERE", you conclude that E= 2.

    At this stage, you can rewrite this puzzle in the form

        HAL1
    +   HAL1
    ----------
       1H2R2

    using what you got in the Step 1.

    Then you conclude that H= 9.  (It can not be nothing else.)

    At this stage, you can rewrite this puzzle in the form

        9AL1
    +   9AL1
    ----------
       192R2

    using what you got in the Steps 1 and 2.

    Then you conclude that A= 6.  (It can not be nothing else.)

    At this stage, you can rewrite this puzzle in the form

        96L1
    +   96L1
    ----------
       192R2

    using what you got in the Steps 1, 2 and 3.

    At this stage, L can be only 3 or 4 and nothing else.  
    Easy analysis excludes L= 3, leaving the only opportunity L= 4, WHICH WORKS (!)