My system is Linux Mint 18.3 Cinnamon 64-bit.
I've installed IntelliJ-IDEA and Default-jdk (openjdk-8-jdk) using the software manager.
I can see what I believe to be the JDK folder under either /usr/lib/jvm/java-1.8.0-openjdk-amd64 or /etc/java-8-openjdk when browsing with the file manager (Nemo) or the terminal. But it doesn't matter because IntelliJ can't see either folder anyway. In fact, when trying to Select Home Directory for JDK, IntelliJ only seems to have visibility to 14 sub-folders (out of hundreds) under /usr/lib.
Not even sure how to launch IDEA from the command-line using sudo, e.g. to test that the issue is permission-related, since it is apparently being launched vicariously via flatpak.
Seems like this should be simple. I'm not sure what I'm doing wrong.
You can try installing IntelliJ IDEA from here and see if it works better. .tar.gz distribution can be launched using ./idea.sh. Note that you can also create a launcher script using Tools>Create Command-line Launcher. This should work with any version.