Using SSRS as a front end of an "application" is not advisable. That said, sometimes you only have a hammer and those screws are going in by themself.
If you are looking for an in-line edit, you are out of luck with anything vanilla (and something like injecting jQuery is very strawberry). You can, however, create a link to a secondary report that is solely used for collecting the input (through parameters), then updating the source data for your report. After the user has entered the data, they need to click 'View Report', which isn't a great experience, but doable. The report results would be a confirmation of the change you just made
Going back to the original report can be tricky. If it lacks any parameters, you can provide a link back to it. If it has parameters, however, you need to build the URL to get back to the original report (include parameters) and include that as an argument to your "line edit" form. Your "line edit" form then will use that for providing a link back. You will have to use
http://ssrs/Reports/Pages/Report.aspx which means that all bread crumbs go away.
Side note: if you are trying to edit, and start with an initial value (e.g. the value you want to change as the starting point), add a 'confirm' dropdown with 1 value not defaulted. This will require the user to change it, but will prevent the form from auto "viewing" which will call your update SQL.