You are right - you move the needle w/the stitches to your left hand then cast on. You'll have to knit the new 18 stitches just cast on first.
Could it be that they only want you to knit the first 19 of the total 37 stitches? -making a short row. Without seeing the pattern or knowing more about what you are making, it's hard to know if it's an error or not. Can you post a link to the pattern or picture of it?
Mirl56 at Ravelry, too.
Learn from the mistakes of others. You canít live long enough to make them all yourself. Eleanor Roosevelt
Lady Feb Sweater
more shawlettes, socks