Answer
E is in the -z direction.
Work Step by Step
To find the direction of the electromagnetic wave, we can find $E \times B$
To apply the right hand rule to electromagnetic waves, the thumb points in the direction of the electric field, the index finger points in the direction of the magnetic field, and the palm faces toward the direction of the wave's motion.
If the palm faces in the -y direction, and the index finger points in the +x direction, then the thumb points in the -z direction.
E is in the -z direction.
