The SE Runtime means that you're running Java Standard Edition, rather than Enterprise Edition (AKA Servlets/JSP, which need an application server). You should be just fine with what you have installed right now! If you want to develop Java programs, just make sure that javac is installed on your system.

EDIT Also, make sure that javac is being provided by java-6-sun, otherwise you'll probably be using the GNU Java compiler which doesn't seem to be what you want.

To Answer the question

The answers and some comments focus on how to set JAVA_HOME to version 11 but the question is partly about "where is version 8 being set?". To answer that see:

• `grep`ing all files for a string takes a long time

Use this command:

$ sudo grep -rnw --exclude-dir={boot,dev,lib,media,mnt,proc,root,run,sys,/tmp,tmpfs,var} '/' -e '/usr/lib/jvm/java-8-oracle' | grep JAVA_HOME

/etc/profile.d/jdk.sh:4:export JAVA_HOME=/usr/lib/jvm/java-8-oracle
/etc/profile.d/jdk.csh:4:setenv JAVA_HOME /usr/lib/jvm/java-8-oracle
/home/rick/.gradle/daemon/4.6/daemon-14831.out.log:53:20:45:23.553 [DEBUG] (... SNIP ...) /usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games:/snap/bin:/usr/lib/jvm/java-8-oracle/bin:/usr/lib/jvm/java-8-oracle/db/bin:/usr/lib/jvm/java-8-oracle/jre/bin (... SNIP ...) Configuring env variables: {PATH=/home/rick/bin:/home/rick/.local/bin:/mnt/e/bin:/mnt/e/usr/local/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games:/snap/bin:/usr/lib/jvm/java-8-oracle/bin:/usr/lib/jvm/java-8-oracle/db/bin:/usr/lib/jvm/java-8-oracle/jre/bin,  (... SNIP ...) 

This is what my system returns. Yours will likely be different. To make a long story short the culprit is /etc/profile.d/jdk.sh:

$ cat /etc/profile.d/jdk.sh

setenv J2SDKDIR /usr/lib/jvm/java-8-oracle
setenv J2REDIR /usr/lib/jvm/java-8-oracle/jre
setenv PATH ${PATH}:/usr/lib/jvm/java-8-oracle/bin:/usr/lib/jvm/java-8-oracle/db/bin:/usr/lib/jvm/java-8-oracle/jre/bin
setenv JAVA_HOME /usr/lib/jvm/java-8-oracle
setenv DERBY_HOME /usr/lib/jvm/java-8-oracle/db

You probably surmise /etc/profile.d/jdk.csh needs changing too. Indeed it contains the exact same contents as /etc/profile.d/jdk.sh

To address the XY problem

There is a better way than going through files line by line and changing an 8 to an 11.

The easiest method is using Java installer. From this Ask Ubuntu Q&A: Setting JDK 7 as default

To get a list of your installed Java platforms, run the following command from the terminal:

sudo update-alternatives --config java

This will give you a list output similar to this:

There are 2 choices for the alternative java (providing /usr/bin/java).
   Selection    Path                                           Priority   Status
  ------------------------------------------------------------
  0            /usr/lib/jvm/java-6-oracle/jre/bin/java         1070      auto mode
  1            /usr/lib/jvm/java-7-openjdk-i386/jre/bin/java   1051      manual mode
* 2            /usr/lib/jvm/java-6-openjdk-i386/jre/bin/java   1069      manual mode
Press enter to keep the current choice[*], or type selection number: