If by 'open' you mean 'extract data out of' then there's a couple of ways - assuming it's an xslx file, not xls.
Essentially modern office documents are zip files containing the content of the document, mostly xml. Try renaming a document to have a .zip extension and take a look if you like. The format is
Office Open XM[
^] standard, since it's developed by Microsoft it has good support in the .Net Framework - although since it's an open standard you could probably extract data out of it using JavaScript in the browser - something like this
Open XML SDK for JavaScript | Eric White[
^]
If you actually need to edit the spreadsheet, I would probably see what you can do to integrate your application with either Office 365 or Google Docs to leverage their functionality, because building a functional spreadsheet application in a browser is probably a lot more work than it seems like.