Brainteaser 1510: Sum puzzle

From The Sunday Times, 18th August 1991 [link]

In this addition sum nine digits are each represented by a different letter and the remaining one digit it represented in various places by nine letters.

When the 47-figure number:

INTHISADDITIONSUMNINEDIGITSAREEACHREPRESENTEDBY

is added to the 46-digit number:

ONELETTERANDONEDIGITISREPRESENTEDBYNINELETTERS

the answer is the 47-figure number:

TDODRRITECIPADAABSDLOTRSORANOHMIAGSAOTUDAYDOEOE

What is the SOLUTION?

The text of this puzzle is taken from the book Brainteasers (2002, edited by Victor Bryant), so may differ from the puzzle originally published in the newspaper.

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