Just as I thought. You're screwed! You have to install another layer of 5/8" plywood underlayment. It needs to be exposure 1 grade C/C/ plugged or better. Do NOT buy CDX grade, it is not for subfloors, it's for sheathing. Once it's properly installed you can then install either a 1/4" backer board or an isolation membrane such as Ditra. Then your tiles.
BTW, you can not install anything directly over a single 1/2" ply, not even carpeting.
Tile 4 You LLC Troy, MI
DITRA Installs - KERDI Watertight-Mold-Free Showers. I have NEVER made a mistake, I thought I did ONCE, but, I was WRONG!A+ BBB rating - est. 1987 - over 50 yrs. exp.