Brainteaser 1635: Double anagram

From The Sunday Times, 9th January 1994 [link]

In the woodwork class the ABLEST students made STABLE TABLES.

In the arithmetic class the cleverest students took those three six-letter words which were anagrams of each other, and they then assigned a different digit to each of the six letters involved. Substituting letters for digits then gave them three six-figure numbers.

They found that one of the numbers was the sum of the other two. Furthermore, no matter what alternative substitution of digits they had used, they could never have achieved this coincidence with a lower sum.

(a) Which word was the sum?
(b) What was its numerical value?

This puzzle was included in the book Brainteasers (2002, edited by Victor Bryant). The text was changed slightly, but the puzzle remains the same.