Install openjdk-8-jdk. Jenkins technically supports Java 8 and Java 11, however several plugins appear to still have compatibility issues so Java 8 is sadly your best bet.

sudo apt install openjdk-8-jdk

Check your alternatives and make sure Java 8 is the default:

rcw@xps:~$ sudo update-alternatives --config java
There are 2 choices for the alternative java (providing /usr/bin/java).

  Selection    Path                                            Priority   Status
* 0            /usr/lib/jvm/java-12-openjdk-amd64/bin/java      1211      auto mode
  1            /usr/lib/jvm/java-12-openjdk-amd64/bin/java      1211      manual mode
  2            /usr/lib/jvm/java-8-openjdk-amd64/jre/bin/java   1081      manual mode

Press <enter> to keep the current choice[*], or type selection number: 2
update-alternatives: using /usr/lib/jvm/java-8-openjdk-amd64/jre/bin/java to provide /usr/bin/java (java) in manual mode

Import the Jenkins repo key:

wget -q -O - | sudo apt-key add -

Add the Jenkins repo to your apt sources:

echo deb binary/ | sudo tee /etc/apt/sources.list.d/jenkins.list

Update and install Jenkins:

sudo apt update
sudo apt install jenkins

Jenkins should now be running:

rcw@xps:~$ systemctl status jenkins
‚óŹ jenkins.service - LSB: Start Jenkins at boot time
   Loaded: loaded (/etc/init.d/jenkins; generated)
   Active: active (exited) since Fri 2019-03-22 08:56:47 PDT; 2min 7s ago
     Docs: man:systemd-sysv-generator(8)
    Tasks: 0 (limit: 4915)
   Memory: 0B
   CGroup: /system.slice/jenkins.service

Go to http://localhost:8080 and follow the on-screen instructions to finish setup.