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Default Need formulas for searching for a value in a table and returning row/column name

I manage a maintenance schedule for equipment. I have a table with 11 columns and about 80 rows. The top row lists the equipment name. The left most column lists the type of maintenance required. The intersecting cells in the table have the date which the maintenance for the particular piece of equipment is due to be done. Some of the dates in the cells occur more than once and some cells are blank. I need 2 formulas, one which return the equipment name (top row) for the first occurrence of a specific date entered in a cell on the worksheet and one which will do the same for the work required (left most column). If the formula fails to find a date, it needs to return a blank space in the cell.
 
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