It is not possible.
It is not possible to create an exe that will run on any computer. Period.
It is possible to create an exe that will run on a Windows machine (I hesitate to say any Windows) but that exe won't run on Linux or Mac OSX ... or any machine that is not a x86 or x86-64 machine (depending on how you built the exe).
It is possible to run a Java application (from a JAR file) on any machine with Java preinstalled.
It is possible to create an exe wrapper for a Java application (see How can I convert my Java program to an .exe file?), but the exe won't that can run on any machine. Like all exe files, it will only run on specific operating systems / hardware architectures. And converting to an exe like this may cause some aspects of Java not to work.
I would recommend these alternatives:
Distribute your application as a JAR file, and leave it up to the user to download and install a JRE separately. (That is NOT hard to do.)
Use an installer-builder (such as InstallAnywhere) to create installers for your application for the platforms you want to support. Use the option for embedding a JRE in the installer.
The other issue is that applet support is going to be removed entirely from Java pretty soon. Indeed, it has already been de-supported in most modern browsers. You should be looking to rewrite your UI code using AWT / Swing, JavaFX, HTML5 or something else.