Linear charge density (what equation?)

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magnitude of 190.2 V/m, with components Ex = -34.23 V/m and Ey = -155.32 V/m.

Oh, I didn't include this numbers before...didn't think they were applicable. Sorry, I'm stuck :(

So, E = the above equation for lambda1 + lambda2?
 
Try drawing a sketch of the individual E vectors from each rod at point P. These have to add as vectors to the total E. (You might have to allow for a negative charge density on a rod.)