I ran into a similar issue with Ubuntu 20.04, downgrading from 5.8 to 5.4 kernel.
I think the answer for 18.04 is similar to @nobody's answer, but you want to specify a slightly different package naming:
sudo apt install linux-generic-hwe-16.04
That one will pull in some things that are needed, along with the 4.15 kernel, though I didn't dig to find further what those things actually are. (the hwe-18.04 package would pull in the mainline kernel for 18.04, which was 5.3 and is now 5.4, I believe)
For completeness, you may want to also install other packages of that sort, namely:
sudo apt install linux-generic-hwe-16.04 \
linux-headers-generic-hwe-16.04 \
linux-image-generic-hwe-16.04
You may also in this scenario want to prevent upgrades to any major kernel above 4.15. You can do that by putting an apt-mark hold on the hwe-18.04 packages. More on that in my answer to this question about holding back the Linux kernel on Ubuntu.