Is there a more elegant way to catch a generic exception than using try-catch block? Here are two sample blocks of my code:

function FindTheNumberOfAddedItems ( PageObj, ItemType )
{
    var localPageObj = PageObj;
    var localItemType = ItemType;
    var numberOfAddedItems = 0;
    var NROCssSelector  = "div[class='assessment-stub list-top-border-colour-1 clearfix box-shadow'] strong";
    var OROCssSelector  = "div[class='assessment-stub list-top-border-colour-2 clearfix box-shadow'] strong";
    var RCCssSelector  = "div[class='assessment-stub list-top-border-colour-3 clearfix box-shadow'] strong";

    try {
        switch (localItemType)
        {
            case "NRO":
                numberOfAddedItems = ParseNumberOutOfString(localPageObj.QuerySelector(NROCssSelector).innerText);
                break;
            case "ORO":
                numberOfAddedItems = ParseNumberOutOfString(localPageObj.QuerySelector(OROCssSelector).innerText);
                break;
            case "RC":
                numberOfAddedItems = ParseNumberOutOfString(localPageObj.QuerySelector(RCCssSelector).innerText);
                break;
            default:
                Log.Message("Invalid item type");
        }
    }
    catch (err){
        Log.Message("Can not find then number of added items.");
    }
    return numberOfAddedItems;
}

function ParseNumberOutOfString ( TextString )
{
    var localTextString = TextString;
    var numberOnlyRegexPattern = /\d+/g;

    try {
        return localTextString.match(numberOnlyRegexPattern);
    }
    catch (err){
        Log.Message("Can not parse number out of string.");
    }
}


I have used try-catch blocks for both functions (and for the rest of all of my functions) in case there is anything wrong with my code.

Come to think about it, having try-catch blocks everywhere is kind of messy. Is there another more elegant way to do it?
@HristoYank is correct, you shouldn't catch exceptions that you can't handle. What you are doing is basically just ignoring the error, which will make it difficult to trace bugs.

If I call a method called ParseNumberOutOfString, I will expect to get a number back. If the function can't return a number, I need to know that, so that I can react appropriately. 

Depending on the situation, I may want to use a default value, ask the user for new input, or abort with an appropriate error message. 

If the function just swallows the error and logs it somewhere, I will continue processing with invalid data (null in this case), which will result in all sorts of bugs down the line. As only a generic error message and no stracktrace is logged, debugging will also be rather difficult.

Misc


match doesn't actually throw an exception, so you will never get into the catch.
don't uppercase your variable names.