If you always have that datetime format I'd suggest a simple regex
"28/08/2015 11:37:47".split(/\/|\s|:/)
This splits it on a / a space and the colon
and will return
["28", "08", "2015", "11", "37", "47"]
Edit as per question asked in comment
function parse() {
/** INPUT FORMAT NEEDS TO BE DAY/MONTH/YEAR in numbers for this to work **/
var datetime= document.getElementById("datetime").value;
var time = document.getElementById("time").value;
var output = document.getElementById("output")
var datetimearr = datetime.split(/\/|\s|:/);
var timearr = time.split(/:/);
var date = new Date(datetimearr[2],datetimearr[1]-1,datetimearr[0],datetimearr[3],datetimearr[4],datetimearr[5]);
date.setHours(date.getHours()+(parseInt(timearr[0])));//parseInt needed otherwise it will default to string concatenation
date.setMinutes(date.getMinutes()+(parseInt(timearr[1])));
date.setSeconds(date.getSeconds()+(parseInt(timearr[2])));
output.value = date.toString();
}
Date time: <input type="text" value="28/08/2015 11:37:47" id="datetime"><BR/>
Time to add: <input type="text" value="11:37:47" id="time"><input type="button" value="calculate!" onclick="parse()"><BR/>
<textarea id="output" placeholder="Output comes here" style="width:400px;height:100px;"></textarea>