Range of numbers

APL (39)

'QWERT'/⍨1↓⊃≠/1 0⌽¨0,¨0 7 18 32 135∘<¨⎕

Takes input as two whitespace-separated numbers.

Explanation:

• 0 7 18 32 135∘<¨⎕: For each number in the input, see if 0, 7, 18, 32, and/or 135 is smaller than the number. If the input was 5 27 we now have (1 0 0 0 0) (1 1 1 0 0). (The first one is taken to be the start of the line and the second one the end).
• 1 0⌽¨0,¨: Prefix a zero to each of those lists and rotate the first one left by 1. (We now have (1 0 0 0 0 0) (0 1 1 1 0 0)).
• ≠/: Gives a list where the individual items of the two input lists were not equal. (We now have 1 1 1 1 0 0).
• 1↓⊃: Remove the first item from this list. The other five stand for whether or not to display a Q, W, E, R or T.
• 'QWERT'/⍨: For each letter, output N of those letters, where N is the corresponding value in the list on the right. Since the list was 1 1 1 0 0 the answer is QWE.

Python 82 84

There you are. Edit: Fixed for inputs like -1 10 and -10 -1 for 2 chars

z=lambda a:(a>7)+(a>18)+(a>32)+(a>135)+1
a,b=input()
print"QWERT"[z(a)-1:z(b)*(b>0)]

GolfScript (43 32 30 chars)

Contains escape characters. As a hex dump:

00000000  7e 29 27 51 08 57 0b 45  0e 52 67 27 32 2f 7b 29  |~)'Q.W.E.Rg'2/{)|
00000010  2a 7d 25 27 54 27 32 24  2a 2b 3c 3e 2e 26        |*}%'T'2$*+<>.&|

Base-64 encoded:

fiknUQhXC0UOUmcnMi97KSp9JSdUJzIkKis8Pi4m

Using bold to indicate escape characters:

~)'Q^HW^KE^NRg'2/{)*}%'T'2$*+<>.&

Thanks to Howard for the suggestion to use escape characters.