  We determine the distances to 18 galaxy clusters with redshifts ranging from
z~0.14 to z~0.78 from a maximum likelihood joint analysis of 30 GHz
interferometric Sunyaev-Zel'dovich effect (SZE) and X-ray observations. We
model the intracluster medium (ICM) using a spherical isothermal beta model. We
quantify the statistical and systematic uncertainties inherent to these direct
distance measurements, and we determine constraints on the Hubble parameter for
three different cosmologies. These distances imply a Hubble constant of 60 (+4,
-4) (+13, -18) km s-1 Mpc-1 for an Omega_M = 0.3, Omega_Lambda = 0.7 cosmology,
where the uncertainties correspond to statistical followed by systematic at 68%
confidence. With a sample of 18 clusters, systematic uncertainties clearly
dominate. The systematics are observationally approachable and will be
addressed in the coming years through the current generation of X-ray
satellites (Chandra & XMM-Newton) and radio observatories (OVRO, BIMA, & VLA).
Analysis of high redshift clusters detected in future SZE and X-ray surveys
will allow a determination of the geometry of the universe from SZE determined
distances.
