T=1823
G5 = (-17000 - 32.0*T)
G6 = (-86100 - 205.1*T)
G7 = (-18120 - 18.62 T)
G8 = (-16400 - 26.8 T)
G9 = (-17430 - 37.2 T)
G10=(−129790.8−54.60T)
G11=(−108019.44−46.56T)
G12=(−75362.4−20.77T)
G13=(−109694.16−0.67T)
G14=(−176749.5+58.27T)
G15=(−91712
+3
0.097T)
G16=(-123985.4+22.3T)
G17=(-147959+22.3T)
G18=(-282626.4+35.28T)
K5 = (E^(-G5/(8.314*T)))
K6 = (E^(-G6/(8.314*T)))
K7 = (E^(-G7/(8.314*T)))
K8 = (E^(-G8/(8.314*T)))
K9 = (E^(-G9/(8.314*T)))
K10 = (E^(-G10/(8.314*T)))
K11 = (E^(-G11/(8.314*T)))
K12 = (E^(-G12/(8.314*T)))
K13 = (E^(-G13/(8.314*T)))
K14 = (E^(-G14/(8.314*T)))
K15 = (E^(-G15/(8.314*T)))
K16 = (E^(-G16/(8.314*T)))
K17 = (E^(-G17/(8.314*T)))
K18 = (E^(-G18/(8.314*T)))
N5 = (K5*N1^3*N3)
N6 = (K6*N1^12*N3^7)
N7 = (K7*N1*N3)
N8 = (K8*N1*N3^2)
N9 = (K9*N1\[CenterDot]N3^6)
N10 = (K10*N1^3*N4)
N11 = (K11*N1^2*N4)
N12 = (K12*N1*N4)
N13 = (K13*N1*N4^2)
N14 = (K14*N3^9*N4^2)
N15 = (K15*N3^2*N4)
N16 = (K16*N2^0.5*N3^0.5)
N17 = (K17*N2^0.5*N3^4.5)
N18 = (K18*N2*N3^3)
Solve[{N1 + N2 + N3 + N4 + N5 + N6 + N7 + N8 + N9 + N10 + N11 + N12 +
N13 + N14 + N15 + N16 + N17 + N18 ==
1 && (0.5*N1 + 3*N5 + 12*N6 + N7 + N8 + N9 + 3*N10 + 2*N11 + N12 +
N13)*U == 0.536 &&
((1/3)*N2 + 0.5*N16 + 0.5*N17 + N18)*U == 0.323 &&
(N3 + N5 + 7 N6 + N7 + 2*N8 + 6*N9 + 9*N14 + 2*N15 + 0.5*N16 +
4.5*N17 + 3*N18)*U == 0.412 &&
(N4 + N10 + N11 + N12 + 2*N13 + 2*N14 + N15)*U == 0.115 && N1 > 0 &&
N2 > 0 && N3 > 0 && N4 > 0 && U > 0}, {N1, N2, N3, N4, U}, Reals]
刚学习这个软件，解不出来数值，请教一下各位！多谢！

既然涉及非精确数，你可能其实不需要解析解
用FindRoot试试看