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If any problems posted in this forum have not been solved, the most probable reason is that the problems were not correctly or clearlly formulated, but not that they are too hard. The correct and clear formulation of your problems makes great sense to prepare yourself one step forward. For youeself, you will have the final chance to review your problems (and last attempt to solve it by yourself) before you appeal to helps. For the forum, this is your chance to show that you are serious about your questions and eager to have someone to help you. Think about it, if you are not serious about your question, why do others bother to look them?
Here are some specifics about your problem which need to work out by yourself:
1. What are the unknows? E or H?
2. WHat are the ranges of i and j?
3. If 1<=i<=N, i<=j<=M, then what are the equations for i=1 and j=1, i=1 and j=M, i=N and j=1, and i=N and j=M. They are special and, usually, need to specify separately.
4, Suppose your questions are something like AX=B, where A is a matrix, and X and B are vectors, then what are A?
Please DO NOT assume that I'll come back revisit your problem even though you make the changes.