Matching different voltage levels using op amp
You need to provide gain and you need to provide an offset.

The gain is \$\dfrac{15 - (-5)}{0.00844 - 0.00344}\$ = 4000

Just applying gain gets you an output signal of 13.76V to 33.76V for the input range of 0.00344V to 0.00844V.

Next you apply an offset and there are plenty of circuits that can do this.

Hint: use an op-amp powered from +36V and 0V to give you the amplification then either use another op-amp to shift the output signals to the desired range or try and figure out how you can use a negative voltage on the first op-amp to get everything done within one op-amp.

Notable is your choice of op-amp - you'll need to choose one with really low offset voltages because any error at the input will be magnified by 4000.