Missing values with Row and Column Totals

Hello everyone,

I'm working with government panel data (yearly data of manufacturing industry (row) by continent (column)) that has a lot (about 10%) missing values that appear to be random. However, I do have the row and column totals, and I do have (in many cases), the surrounding years' values. There are at least two missing values per row and column.

What I have done is used regression analysis on the previous years to obtain the missing values, but I have not been able to utilize the information I have on row and column totals, which would help me greatly with my estimates...it's almost like a sudoku puzzle...

Any suggestions? I think there has to be an algorithm or a program that can use all this info at once.