Birthday!

So, to make a painful story short, years ago on my birthday, my parents and I (still a child) went to visit my Aunt Mildred, who lived alone in a palatial state. Only by remaining in such isolation was she able to get on with all of her co-habitants. Of course, we still visited out of familial obligation(i.e. she gave us money on our birthday.) On a particular birthday, as she reached in her purse, she asked, "Well, how old are you, today?"

"My age would, if squared, equal a number, the sum of whose digits is seven less than my age. So, Aunt Mildred," I asked, jutting my head out like a French aristocrat fresh off the tumbril, "Can you tell me how old I am?"

"No," she replied calmly, withdrawing a big bill and a lighter from her purse. As she set it alight, she replied "But I know what fifty minus fifty is." How old was I on this dark and dreadful birthday?