That's not a big deal at all, I mean - you're not 48, that age difference was probably the smallest in my family tree, starting with my grandparents. My wife, if I'll ever have one, will be younger no less than 8 years, I'd prefer 10-12 tho', current gf younger over 6 years, and I already start to kind of surpass her in the "good body" department (and she's hot, good genes, but needs to ramp up her training if she wants to keep up with me).
My advice - LIE for at least three-four more months, lie through your teeth till she "falls in love" with you, don't listen to these rightful pussies, you don't have anything to loose in this case if you tell her later, rather than sooner. If she happens to really like you, females are emotional creatures, trust me - she'll get over that soon, and what the hell - you are JUST 38 ffs.
I fella I know met his wife 20 years ago, he's 11 years older than her. When they met fucker lied even his name, because he had a gf (and age by 6 years), she figured out like half a year later (yes, even his real name lol).