Show us, in a shell, run
What do you get?
I have jdk10 and sqldeveloper-18.1.0.095.1630-macosx.app and get the same message.
$ java -version
java version "10" 2018-03-20
Java(TM) SE Runtime Environment 18.3 (build 10+46)
Java HotSpot(TM) 64-Bit Server VM 18.3 (build 10+46, mixed mode)
We don't support Java 10 yet, and while we don't officially support java 9 yet, it should work. As long as you're not using the data miner extension.