Edge Difference Sudoku (Daily Sudoku League #58)

I wanted to create a Difference Sudoku for a Sudoku project but I misunderstood instructions to end up creating this Edge Difference Sudoku.
Recently we celebrated World Sudoku Day on 9th September and my previous post titled Happy World Sudoku Day (Classic Sudoku: Fun With Sudoku #16) was to celebrate this Sudoku Day. 
Now, 1st episode of Sudoku Mahabharat is going to start on 20th September 2014. The Mahabharata is one of the most widely read Sanskrit epics in India. The Mahabharata is a wonderful epic with many heroic characters, dramatic incidents, and popular legends. It's very interesting to understand the circumstances in Mahabharata, which forced the characters of Mahabharata to take certain decisions. It was very interesting to analyze and learn from the consequences of these decisions. Mahabharata is a wonderful epic for reading. One interesting thing in Mahabharata I found is that even though it happened thousands of years back, it contains knowledge of all modern war weapons from Fire to Forget Missiles to Atomic Bombs and maybe weapons to be developed in the coming time. Highly recommended read indeed.
This Edge Difference Sudoku is my 58th contribution to The League of Extraordinary Ladies and Gentlemen. Can you solve this Edge Difference Sudoku puzzle?
Rules of Edge Difference Sudoku
Classic Sudoku Rules apply. Additionally, numbers given outside the grid show the differences between the first and last digits in the corresponding row or column.
Edge Difference Sudoku (Daily Sudoku League #58)
Edge Difference Sudoku (Daily Sudoku League #58)

Classic Sudoku  (Fun With Sudoku #16) Solution
Classic Sudoku  (Fun With Sudoku #16) Solution

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