The difference between 850 lines and 1080 lines is almost double. Not 18%. It's not a linear relationship due to both x and y increasing simultaneously in 16:9 ratio.
You're right if we double the horizontal resolution and keep the aspect ratio for the height, we'll square the area: a non-linear x^2 function. You are correct to point out that in terms of the entire image, it's larger than 18%.
1080? As in 1080p vertical resolution? When I write 850 lines, it's vertical black lines (separated by white lines) which define horizontal resolution. >960 ("1000+") lines can resolve 1920 horizontal pixels. 850 lines can resolve 1700 horizontal pixels (850*2: black + white lines). 1700*9/16 = 956, 1700*956 = 1.63 megapixels. 1920*1080 = 2.07 megapixels. Thus, a 27% increase in area.