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Identity by Ordered Subtraction

A number N consists of unique (all different) digits.
Let A be the number formed by putting the digits in descending order.
Let B be the number formed by putting the digits in ascending order.
Find all possible N which satisfy A-B=N.
(Leading zeros are allowed, if needed.)
Are there any additional answers if we remove the requirement that
N consists of unique digits (but still be no more than 10 digits)?

Source: Based on a problem from
Casio's Problem of the Week. Original extensions.

Solution

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