If you want to subtract dates in Excel, it helps to understand the way that Excel stores dates.
Dates are stored as positive integers in Excel. It is only the formatting of an Excel cell that causes its contents to be displayed as a date, rather than an integer.
The numbering system used for Excel dates varies with different computer systems, but most commonly, the numbering system is:
integer  equivalent date (mm/dd/yyyy) 

1  01/01/1900 
2  01/02/1900 
3  01/03/1900 
. . .  
42735  12/31/2016 
As Excel dates are internally stored as simple integers, you can subtract dates in Excel, in the same way that you can subtract any other integers. The result from the subtraction of any two dates is equal to the number of days between the two dates.
Column C of the following spreadsheet shows three examples of Excel date subtraction formulas. In each case, the date in column A is subtracted from the date in column B.
Formulas:
 Results:

Note that, in the results spreadsheet above, the cells in columns A and B are formatted with a date format, but the cells in column C are formatted with the 'General' format.
If the result of your date subtraction is displayed as a date, but you require a simple number, you will need to change the formatting of the results cell, to display the 'General' data type.
The easiest way to do this is to select the General formatting option from the dropdown format menu of the Excel ribbon. This is generally located in the 'Number' group, on the Home tab of the ribbon (see below):