cgilman - I read the reference. The grade is important ONLY for determining the target assembly bolt stress.
Now, I may be taking a bit of leap of faith here, but given that the OP requested information regarding ASME grade bolts, I am going to assume a pressure vessel or piping use. Now, the determination of an appropriate target assembly bolt stress (or load, whatever your fancy) is extremely important, and takes into consideration, among other things, the gasket in the joint.
Now, once you have determined your target assembly bolt stress, you need to calculate a torque. Going from stress (or load) to torque doe NOT involve the grade of bolt. Rather, the grade of bolt was determined from the desired stress. Basically - the bolt doesn't know what grade it is, but with the application of a torque on the nut, it achieves a particular stress.
BTW, my formula for torque is:
T=P*(p_t/2*pi+(mu*d_b)/2*cos(alpha)+mu_n*d_n/2)
where:
T is the torque
P is the bolt's desired tensile load
p_t is the thread pitch
mu is the coefficient of friction between the nut and the bolt (often lubricated)
d_b is the nominal (basic) diameter
alpha is the thread half angle
mu_n is the coefficient of friction between the nut and the flange surface (often not lubricated)
d_n is the mean contact diameter under the nut head (average of the diameter across the flats and across the corners)
Neither in your formula nor mine is there a place for E, or yield strength, or anything that relates to the bolt grade.