Cryptarithmetic problem is a type of mathematical game consisting of arithmetic operations among unknown numbers, whose digits are represented by alphabets. It is generally a number puzzle problem in which a group of arithmetic operations has some or all of its digits replaced by alphabets or symbols (for example, if Z=4, then ZZ=44), and where the original digits must be found . In such a problem, each alphabet or symbol represents a unique digit and arithmetic operations might be addition, multiplication or division.
Here we know that T is not 0, as T+T is not equal to T. The case is same with A. After that we have to solve every letter for the problem making each letter unique. The steps are below.
EAT = 819, THAT = 9219, APPLE =10038
 E. Weisstein (2014). Cryptarithmetic. [Online] Available: http://mathworld.wolfram.com/Cryptarithmetic.html