I am working on a website, coded with html and PHP, that takes input from the user. I want to take this data from the html form and send it to an application installed on the computer, and then receive the document generated by the application using the data. I don't have access to the code of this application (Also not 100% sure which environment was used to code the application, but I will do some digging). Is there a way to do this? If more information is required I will update the question.
No there is not.
Even if you had acces to the code or you programmed it yourself, you should make it listen to a port for incoming requests. The browser is too restricted, fortunately, too let webpages talk directly to applications: think how hackers could abuse it!
What application is it? maybe there are alternatives to the installation on the client computer :-)