Extracting Numbers In Word Format From A String Of Text

I am trying to do is extract numbers that are in word format in a long String, i.e. a song, and return each of their numerical values, in order to add them all up. So I'd like to calculate the sum of all of the numbers in the text. This has to work for any piece of text and for all numbers up to a trillion.

So I broke the string down into tokens and stored them in a String []. And I divided up the possible numbers in word format into:

LARGEST: thousand, million, billion, trillion
HUNDRED: hundred
TENS: twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety
UNITS: one, two, three, four, five, six, seven, eight, nine
SPECIALS: ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen

I believe that these are the only words that it will need to recognize. I began reading the tokenized string from right to left and then when I came across a unit, special or tens as the first number I hit, I would then set it's numerical value and check if the word before was also a number and whether to add or multiply etc. i.e. First number hit is a two, if the number before is sixty, then I would just add it to sixty and check the word before that and so on.

However, when implementing it, it seems like an extremely long way around it. How I could implement this in a swifter manner? An example of it working would be:

"Nine Million rockets turned Three times and met Twenty Two Aliens", it would extract, Twenty Two as 2, then 20 = 22, then extract Three as 3, and then Nine Million as 1,000,000 x 9 = 9,000,000

9,000,000 + 22 + 3 = 9,000,025