Take the E tuner off, get a clamp and dry clamp it too make sure it closes the crack, if it doesn't you may need to make a caul to apply even pressure.
Now once you've figured out how to go about clamping it, take some wood glue (tightbond is good and
make sure your not getting the water proof kind)
and dilute the glue in a small container with water, thin it out too about the thickness of milk, it should look like tan milk.
Get a few water dampened sponges and some dry cloth handy, and start working in the watered down glue.
Be liberal and get a lot of that glue worked in there over about five or so minutes, then wipe away the excess with a sponge and then the dry cloth, clamp wipe again and then let dry for a day.
That will fix the crack in the wood and make it stable, if you want to fix the crack in the finish that's another process.
Best of luck,
Samantha.