One source for the Java 8 (1.8) runtime is the Oracle Archives page.  Another helpful one is the standard Java download page for the desktop Java Runtime Environment, JRE.

I downloaded the Linux x86 (32-bit) version even though the host is a 64bit Linux.  The reason for that is that at some point in the point in the past Minecraft and various mods and the Forge loader required a 32 bit Java virtual machine (JVM).  It was so problematic to install both 64bit and 32bit via the package managers and manually configure them, that I developed a practice of installing 32-bit Linux so that the Java in the repository would also be 32bit and then everything would be fin.   It was much easier to run 32-bit Java and 32-bit Wine on a 32-bit operating system than reconfigure everything and try to switch between them depending on what was running.

I extracted the zip file from Oracle and then ran the Minecraft server instance with the following command.

home/username/Downloads/Java8_i586/jre1.8.0_461/bin/java -jar /home/username/Minecraft_x86/instances/b1.7.3/b1.7.3.251019/b1.7.3.jar nogui

Running the program that way worked very well.