Don't try to suddenly do the whole distance every day.
Start by trying two days per week, say Tuesday and Thursday. Leave plenty of time for your ride and take it easy. Allow a good hour for the journey. Once this becomes easy try three days per week (Monday, Wednesday and Friday), then four days (Monday, Tuesday, Thursday, Friday), then finally every day. For this distance you will be in the realms of needing to take in extra food so have something to eat shortly after you arrive at work, and shortly before you leave for home. Make sure you get a good nights sleep so your legs will recover properly overnight and you will feel refreshed the next morning. You could also try some stretching when you get home which may help with easing soreness.
You may be unlucky and find that you can never do the full journey every day, every week. If so, then just do what you can and don't stress about it.
You may want to consider changing the gearing on your current bike to a lower or wider spread of gears (maybe change the rear cassette) if you find yourself grinding your way up the hills.
One last thing, it WILL be hard work at first. Just persevere through the first few weeks and you will get stronger and fitter, and the journey will get easier.