Painted walls showing darker when dry where painted with brush, than with roller
how can I achieve the same finish using a brush as I did using a roller


In my experience, you can't. I usually find that brushed paint doesn't cover as well as paint applied using a roller. I find it helpful to do the corners first, going slowly. Apply extra coats as necessary. Then use a roller for the main part of the wall and paint as close into the corner as possible. A damp cloth (if water-based emulsion/latex) and a paint-guard can help.

I don't know about you, but I find I am much more fussy about these things when I am doing the work, but after a week I never think about or notice small defects any more.