There`s no way I could honestly answer that question, only the manufacturer of the motherboard will know for sure.
But you find one cheap and take a chance, you put it in and if you see the bios on the screen you know it works
The spec sheet says (E21xx series) but I think they are just talking about the Pentium Dual core, because I can`t find any Core 2 Duo E21xx series at all, so there probably is no such thing.
There was/is a E4xxx series, an E6xxx series, an E7xxx series, and a E8xxx series, so you see how many versions there are, and you have to find out exactly which version your board supports.
OK, I clicked on cpu in the link that barman posted and it brings up all the supported cpu`s.
ECS > G31T-M7 (V1.0)
And all these Core 2 Duo are supported, so yes the E8400 will work, but I`d get the E8600
LGA775 Intel Core 2 Duo E4300 (L2) (65W) N/A 1.80 GHz 2MB N/A 10/02/25
LGA775 Intel Core 2 Duo E4400 (L2) (65W) N/A 2.00 GHz 2MB N/A 10/02/25
LGA775 Intel Core 2 Duo E4400 (M0) (65W) N/A 2.0 GHz 2MB N/A 10/02/25
LGA775 Intel Core 2 Duo E4500 (M0) (65W) N/A 2.20 GHz 2MB N/A 10/02/25
LGA775 Intel Core 2 Duo E4600 (M0) (65W) N/A 2.4 GHz 2MB N/A 10/02/25
LGA775 Intel Core 2 Duo E4700 (G0) (65W) N/A 2.6 GHz 2MB N/A 10/02/25
LGA775 Intel Core 2 Duo E6300 (B2) (65W) N/A 1.86 GHz 2MB N/A 10/02/25
LGA775 Intel Core 2 Duo E6320 (B2) (65W) N/A 1.86 GHz 4MB N/A 10/02/25
LGA775 Intel Core 2 Duo E6400 (B2) (65W) N/A 2.13 GHz 2MB N/A 10/02/25
LGA775 Intel Core 2 Duo E6420 (B2) (65W) N/A 2.13 GHz 4MB N/A 10/02/25
LGA775 Intel Core 2 Duo E6540 (G0) (65W) N/A 2.33 GHz 4MB N/A 10/02/25
LGA775 Intel Core 2 Duo E6550 (G0) (65W) N/A 2.33 GHz 4MB N/A 10/02/25
LGA775 Intel Core 2 Duo E6600 (B2) (65W) N/A 2.40 GHz 4MB N/A 10/02/25
LGA775 Intel Core 2 Duo E6700 (B2) (65W) N/A 2.66 GHz 4MB N/A 10/02/25
LGA775 Intel Core 2 Duo E6750 (G0) (65W) N/A 2.66 GHz 4MB N/A 10/02/25
LGA775 Intel Core 2 Duo E6850 (G0) (65W) N/A 3.00 GHz 4MB N/A 10/02/25
LGA775 Intel Core 2 Duo E7200 (M0) (65W) N/A 2.53GHz 3MB N/A 10/02/25
LGA775 Intel Core 2 Duo E7400 (R0) (65W) N/A 2.80 GHz 3MB N/A 10/02/25
LGA775 Intel Core 2 Duo E7500 (R0) (65W) N/A 2.93 GHz 3MB N/A 10/02/25
LGA755 Intel Core 2 Duo E7600 (R0) (65W) N/A 3.06 GHz 3MB N/A 10/02/25
LGA775 Intel Core 2 Duo E8190 (C0) (65W) N/A 2.66 GHz 6MB N/A 10/02/25
LGA775 Intel Core 2 Duo E8200 (C0) (65W) N/A 2.66 GHz 6MB N/A 10/02/25
LGA775 Intel Core 2 Duo E8300 (C0) (65W) N/A 2.83 GHz 6MB N/A 10/02/25
LGA775 Intel Core 2 Duo E8400 (C0) (65W) N/A 3.00 GHz 6MB N/A 10/02/25
LGA775 Intel Core 2 Duo E8400 (E0) (65W) N/A 3.0 GHz 6MB N/A 10/02/25
LGA775 Intel Core 2 Duo E8500 (C0) (65W) N/A 3.16 GHz 6MB N/A 10/02/25
LGA775 Intel Core 2 Duo E8500 (E0) (65W) N/A 3.16 GHz 6MB N/A 10/02/25
LGA775 Intel Core 2 Duo E8600 (E0) (65W) N/A 3.33 GHz 6MB N/A 10/02/25