Yes, you have to use DateFormat or better SimpleDateFormat to be able to parse your input and to get a Date. This Date you can put into a Calendar, which has the function getTimeInMillis(). This you have to do for both date values. It is easy to substract both millis and to calculate seconds from it. This sounds a bit strange, but in fact it will be not more than 20 lines of code or maybe less. Even much better, than calculating all by yourself.
Watchya got in that poodle gun? Anything for me? Or this tiny ad?
a bit of art, as a gift, the permaculture playing cards